sage cannot get the simplest form on the limit expression with binomial and exponential operations

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considering the flowing code:

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from sage.symbolic.assumptions import GenericDeclaration;

var('lamda,n,k,p');

decl1 = GenericDeclaration(k, 'integer');

decl1.assume();

assume(k>0,k>1,n>k,lamda>0,lamda<n);

ep=binomial(n,k)*p^k*(1-p)^(n-k);

ep=ep.subs_expr(p==lamda/n);

ep=ep.subs_expr(binomial(n,k)==factorial(n)/factorial(k)/factorial(n-k));

ep=limit(ep,n=oo);

ep.simplify_full();

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the result is:

lamda^k*limit((-(lamda - n)/n)^n*factorial(n)/((-lamda + n)^k*factorial(-k + n)), n, +Infinity)/factorial(k)

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it is not the simplest form. In fact , sage will give me the simplest form as below when I paste the result above to sage again.

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lamda^k*e^(-lamda)/factorial(k)

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the question is how can i get the simplest form directly?