A367155 E.g.f. satisfies A(x) = 1 + A(x)^3 * log(1 + x).

1, 1, 5, 56, 948, 21804, 634284, 22348584, 925322784, 44039346264, 2369167375656, 142173632632272, 9416315321258928, 682290228636729504, 53689645309437175968, 4559660591348115191808, 415683140400707316145920, 40490500091575002629253120

Offset: 0

Author

Seiichi Manyama, Nov 07 2023

Keywords

• nonn

Crossrefs

Cf. A367158, A367161, A367164.

Cf. A087152.

Programs

Mathematica

Table[Sum[(3*k)!/(2*k+1)! * StirlingS1[n,k], {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Nov 10 2023 *)

PARI

a(n) = sum(k=0, n, (3*k)!/(2*k+1)!*stirling(n, k, 1));

Formula

a(n) = Sum_{k=0..n} (3*k)!/(2*k+1)! * Stirling1(n,k).

a(n) ~ 9 * n^(n-1) / (2^(5/2) * (exp(4/27) - 1)^(n - 1/2) * exp(n + 2/27)). - Vaclav Kotesovec, Nov 10 2023