A357032 E.g.f. satisfies log(A(x)) = (exp(x * A(x)) - 1)^3 / 6.
1, 0, 0, 1, 6, 25, 160, 1981, 24906, 295625, 4044900, 68136541, 1260048086, 24330807865, 508029259920, 11686882860381, 289532464998146, 7588430921962825, 210991834698749020, 6244230552027963901, 195584639712483465486, 6442981074293371848185
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\3, (3*k)!*(n+1)^(k-1)*stirling(n, 3*k, 2)/(6^k*k!));
Formula
a(n) = Sum_{k=0..floor(n/3)} (3*k)! * (n+1)^(k-1) * Stirling2(n,3*k)/(6^k * k!).