A382804 a(n) = Sum_{k=0..n} k! * (k+1)! * Stirling1(n,k)^2.
1, 2, 14, 260, 9588, 581952, 52096512, 6423520896, 1041005447424, 214260350714496, 54547409318781312, 16820040059243046144, 6175245603727007034624, 2661063379044058584861696, 1329787781176741647226481664, 762665713456216694195942866944
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, k!*(k+1)!*stirling(n, k, 1)^2);
Formula
a(n) == 0 (mod 2) for n > 0.
a(n) = (n!)^2 * [(x*y)^n] 1 / (1 - log(1-x) * log(1-y))^2.
a(n) = (n!)^2 * [(x*y)^n] 1 / (1 - log(1+x) * log(1+y))^2.
a(n) ~ sqrt(Pi) * n^(2*n + 3/2) / (exp(1) - 1)^(2*n+2). - Vaclav Kotesovec, Apr 05 2025