A382678 a(n) = Sum_{k=0..n} (k!)^2 * binomial(k+3,3) * Stirling2(n+1,k+1)^2.
1, 5, 77, 2357, 118061, 8712245, 886143917, 118592620277, 20176999414061, 4249819031692085, 1084956766012858157, 329975948760472311797, 117851658189070970988461, 48830366210401091606537525, 23228207308210113849419226797, 12571433948267218576823401692917
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, k!^2*binomial(k+3, 3)*stirling(n+1, k+1, 2)^2);
Formula
a(n) = (n!)^2 * [(x*y)^n] exp(x+y) / (exp(x) + exp(y) - exp(x+y))^4.