A382739 a(n) = Sum_{k=0..n} (k!)^2 * binomial(k+3,3) * Stirling2(n,k)^2.
1, 4, 44, 1084, 48044, 3281404, 316032044, 40592233084, 6687195379244, 1372291071723004, 342877475325619244, 102409872018962876284, 36014541870868393113644, 14724003012156426011095804, 6922777830859189006847193644, 3708347961746448904830944962684
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, k!^2*binomial(k+3, 3)*stirling(n, k, 2)^2);
Formula
a(n) == 0 (mod 4) for n > 0.
a(n) = (n!)^2 * [(x*y)^n] 1 / (exp(x) + exp(y) - exp(x+y))^4.