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 | 1 | initial version |
Sage offers various ways to express the desired product, using
- factorial
- gamma
- falling factorial
- rising factorial
- product
- held product
Only the last one seems to keep the desired product expressed as a product of n + 2 terms.
sage: k, n = SR.var('k, n')
sage: factorial(2*n + 3)/factorial(n + 1)
factorial(2*n + 3)/factorial(n + 1)
sage: gamma(2*n + 4)/gamma(n + 2)
gamma(2*n + 4)/gamma(n + 2)
sage: falling_factorial(2*n + 3, n + 2)
gamma(2*n + 4)/gamma(n + 2)
sage: rising_factorial(n + 2, n + 2)
gamma(2*n + 4)/gamma(n + 2)
sage: product(k, k, n + 2, 2*n + 3)
factorial(2*n + 3)/factorial(n + 1)
sage: product(k, k, n + 2, 2*n + 3, hold=True)
product(k, k, n + 2, 2*n + 3)
