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%I #15 Apr 08 2024 18:50:07
%S 1,1,1,2,6,8,40,720,1680,13440,362880,1209600,4435200,68428800,
%T 296524800,29059430400,1307674368000,6974263296000,118562476032000,
%U 6402373705728000,445586448384000,1430277488640000,51090942171709440000,374666909259202560000,8617338912961658880000
%N a(n) = denominator(Sum_{k=1..n} k^2/k!).
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IncompleteGammaFunction.html">Incomplete Gamma Function</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Incomplete_gamma_function#Upper_incomplete_Gamma_function">Incomplete gamma function</a>.
%F a(n) = denominator((2*(e*Gamma(n+1, 1) - 1) - n)/n!).
%F a(n) = denominator(A030297(n)/n!).
%F Limit_{n->oo} A371831(n)/a(n) = 2*e = A019762.
%t a[n_]:=Denominator[(2(E*Gamma[n+1,1]-1)-n)/n!]; Array[a,25,0]
%o (PARI) a(n) = denominator(sum(k=1, n, k^2/k!)); \\ _Michel Marcus_, Apr 07 2024
%Y Cf. A019762, A030297, A371831.
%Y Cf. A014973, A092043.
%K nonn,frac
%O 0,4
%A _Stefano Spezia_, Apr 07 2024
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