restart;
a := n -> n!*(1+hypergeom([-n+1],[-n],-1))-(n!-GAMMA(n+1,-1)/exp(1)): simplify(expand(a(n)));
seq(simplify(expand(a(n))),n=1..9);
1, 2, 5, 20, 97, 574, 3973, 31520, 281825
# OK, so let's take the simplification proposed by Maple!
a1 := n -> exp(-1)*(GAMMA(n+2)+GAMMA(n+1, -1)*n)/n; seq(simplify(expand(a1(n))),n=1..9);
2*exp(-1), 3*exp(-1)+1, 8*exp(-1)+2, 30*exp(-1)+9, 144*exp(-1)+44, 840*exp(-1)+265, 5760*exp(-1)+1854, 45360*exp(-1)+14833, 403200*exp(-1)+133496
I will submit a bug report.
Am Mittwoch, 4. Oktober 2017 21:57:43 UTC+2 schrieb acer:
I will submit a bug report.
Great!
But do not think this is an isolated error.
Maple is not able to compute even the most elementary
hypergeometrics correctly. Just another one of many,
many I have encountered in the recent years:
T := (n,k) -> n!*hypergeom([k - n], [-n], -1);
for n from 0 to 6 do seq(simplify(T(n,k)),k=0..n) od;
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