A367161 E.g.f. satisfies A(x) = 1 + A(x)^3 * (exp(x) - 1).

1, 1, 7, 91, 1795, 47851, 1612027, 65731891, 3148530595, 173319612571, 10782796483147, 748237171338691, 57299882326956595, 4800323120225595691, 436719009263680421467, 42878536726317406241491, 4519124182661042439577795, 508885588456024192452993211

Offset: 0

Author

Seiichi Manyama, Nov 07 2023

Keywords

• nonn

Crossrefs

Cf. A367155, A367158, A367164.

Cf. A052895.

Programs

Mathematica

Table[Sum[(3*k)!/(2*k+1)! * StirlingS2[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, 2));

Formula

a(n) = Sum_{k=0..n} (3*k)!/(2*k+1)! * Stirling2(n,k).

a(n) ~ sqrt(93) * n^(n-1) / (2^(5/2) * log(31/27)^(n - 1/2) * exp(n)). - Vaclav Kotesovec, Nov 10 2023