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### An Exercicse from A=B

Let r(n,k) = -k^2(3n+3-2k)/(2(n+1-k)^2(2n+1)) f(n,k)=factorial(n)^4/(factorial(k)^2factorial(n-k)^2factorial(2n)) g(n,k)=r(n,k)f(n,k) from Petkovsek, Wilf & Zeilberger's A=B.

The authors show how to use Mathematica or Maple to prove that f(n+1,k)-f(n,k)-g(n,k+1)+g(n,k) is zero for any integer values of k and n.

I am not able to prove this with Sage (10.3). Any idea?

### An Exercicse from A=B

Let r(n,k) = -k^2(3n+3-2k)/(2(n+1-k)^2(2n+1)) f(n,k)=factorial(n)^4/(factorial(k)^2factorial(n-k)^2factorial(2n)) g(n,k)=r(n,k)f(n,k) from Petkovsek, Wilf & Zeilberger's A=B. , p. 27-29.

The authors show how to use Mathematica or Maple to prove that f(n+1,k)-f(n,k)-g(n,k+1)+g(n,k) is zero for any integer values of k and n.

I am not able to prove this with Sage (10.3). Any idea?

### An Exercicse from A=B

Let

r(n,k) = -k^2(3n+3-2k)/(2(n+1-k)^2(2n+1)) n+1))

f(n,k)=factorial(n)^4/(factorial(k)^2factorial(n-k)^2factorial(2n)) g(n,k)=r(n,k)f(n,k) factorial(2*n))

g(n,k)=r(n,k)*f(n,k)

from Petkovsek, Wilf & Zeilberger's A=B, p. 27-29.

The authors show how to use Mathematica or Maple to prove that f(n+1,k)-f(n,k)-g(n,k+1)+g(n,k) is zero for any integer values of k and n.

I am not able to prove this with Sage (10.3). Any idea?

 4 None vdelecroix 7620 ●20 ●84 ●168 http://www.labri.fr/pe...

### An Exercicse from A=B

Let

r(n,k) $$r(n,k) = -k^2(3n+3-2k)/(2(n+1-k)^2(2n+1))n+1))$$

f(n,k)=factorial(n)^4/(factorial(k)^2$$f(n,k)=factorial(n)^4/(factorial(k)^2factorial(n-k)^2factorial(2*n))factorial(2*n))$$

g(n,k)=r(n,k)*f(n,k)$$g(n,k)=r(n,k)*f(n,k)$$

from Petkovsek, Wilf & Zeilberger's A=B, p. 27-29.

The authors show how to use Mathematica or Maple to prove that f(n+1,k)-f(n,k)-g(n,k+1)+g(n,k) is zero for any integer values of k and n.

I am not able to prove this with Sage (10.3). Any idea?

 5 None vdelecroix 7620 ●20 ●84 ●168 http://www.labri.fr/pe...

### An Exercicse from A=B

Let

$$r(n,k) r(n,k) = -k^2(3n+3-2k)/(2(n+1-k)^2(2n+1))$$n+1))$$$f(n,k)=factorial(n)^4/(factorial(k)^2f(n,k)=factorial(n)^4/(factorial(k)^2factorial(n-k)^2factorial(2*n))$$factorial(2*n))$

$$g(n,k)=r(n,k)*f(n,k)$$$g(n,k)=r(n,k)*f(n,k)$

from Petkovsek, Wilf & Zeilberger's A=B, p. 27-29.

The authors show how to use Mathematica or Maple to prove that f(n+1,k)-f(n,k)-g(n,k+1)+g(n,k) is zero for any integer values of k and n.

I am not able to prove this with Sage (10.3). Any idea?

 6 None vdelecroix 7620 ●20 ●84 ●168 http://www.labri.fr/pe...

### An Exercicse from A=B

Let

$r(n,k) r(n,k) = -k^2(3n+3-2k)/(2(n+1-k)^2(2n+1))$n+1))

$f(n,k)=factorial(n)^4/(factorial(k)^2f(n,k)=factorial(n)^4/(factorial(k)^2factorial(n-k)^2factorial(2*n))$factorial(2*n))

$g(n,k)=r(n,k)*f(n,k)$g(n,k)=r(n,k)*f(n,k)

from Petkovsek, Wilf & Zeilberger's A=B, p. 27-29.

The authors show how to use Mathematica or Maple to prove that f(n+1,k)-f(n,k)-g(n,k+1)+g(n,k) is zero for any integer values of k and n.

I am not able to prove this with Sage (10.3). Any idea?

 7 None vdelecroix 7620 ●20 ●84 ●168 http://www.labri.fr/pe...

### An Exercicse from A=B

Let

r(n,k) $r(n,k) = -k^2(3(3n+3-2k)/(2n+3-2k)/(2(n+1-k)^2(2n+1))(n+1-k)^2 (2n+1))$

f(n,k)=factorial(n)^4/(factorial(k)^2factorial(n-k)^2factorial(2*n))

g(n,k)=r(n,k)*f(n,k)$g(n,k)=r(n,k)*f(n,k)$

from Petkovsek, Wilf & Zeilberger's A=B, p. 27-29.

The authors show how to use Mathematica or Maple to prove that f(n+1,k)-f(n,k)-g(n,k+1)+g(n,k) is zero for any integer values of k and n.

I am not able to prove this with Sage (10.3). Any idea?

 8 None vdelecroix 7620 ●20 ●84 ●168 http://www.labri.fr/pe...

### An Exercicse from A=B

Let

$r(n,k)$ r(n,k) = -k^2(3n+3-2k)/(2(n+1-k)^2 (2n+1))$-k^2 (3n+3-2k) / (2*(n+1-k)^2 (2n+1))$

f(n,k)=factorial(n)^4/(factorial(k)^2$f(n,k) =\frac{factorial(n)^4}{factorial(k)^2factorial(n-k)^2factorial(2*n))factorial(2*n)}$

$g(n,k)=r(n,k)*f(n,k)$$g(n,k)=r(n,k)*f(n,k)$

from Petkovsek, Wilf & Zeilberger's A=B, p. 27-29.

The authors show how to use Mathematica or Maple to prove that f(n+1,k)-f(n,k)-g(n,k+1)+g(n,k) is zero for any integer values of k and n.

I am not able to prove this with Sage (10.3). Any idea?

 9 None vdelecroix 7620 ●20 ●84 ●168 http://www.labri.fr/pe...

### An Exercicse from A=B

Let

$r(n,k) = -k^2 (3n+3-2k) / (2*(n+1-k)^2 (2n+1))$

$f(n,k) =\frac{factorial(n)^4}{factorial(k)^2factorial(n-k)^2factorial(2*n)} =\frac{n!^4}{k!^2 (n-k)!^2 (2n)!}$

$g(n,k)=r(n,k)*f(n,k)$

from Petkovsek, Wilf & Zeilberger's A=B, p. 27-29.

The authors show how to use Mathematica or Maple to prove that f(n+1,k)-f(n,k)-g(n,k+1)+g(n,k) is zero for any integer values of k and n.

I am not able to prove this with Sage (10.3). Any idea?

 10 None vdelecroix 7620 ●20 ●84 ●168 http://www.labri.fr/pe...

### An Exercicse from A=B

Let

$r(n,k) = -k^2 (3n+3-2k) / (2*(n+1-k)^2 (2(n+1-k)^2 (2n+1))$

$f(n,k) =\frac{n!^4}{k!^2 (n-k)!^2 (2n)!}$

$g(n,k)=r(n,k)*f(n,k) g(n,k)=r(n,k) f(n,k)$

from Petkovsek, Wilf & Zeilberger's A=B, p. 27-29.

The authors show how to use Mathematica or Maple to prove that f(n+1,k)-f(n,k)-g(n,k+1)+g(n,k) is zero for any integer values of k and n.

I am not able to prove this with Sage (10.3). Any idea?