A367161 - OEIS

%I #11 Nov 10 2023 04:12:21

%S 1,1,7,91,1795,47851,1612027,65731891,3148530595,173319612571,

%T 10782796483147,748237171338691,57299882326956595,4800323120225595691,

%U 436719009263680421467,42878536726317406241491,4519124182661042439577795,508885588456024192452993211

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

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

%F a(n) ~ sqrt(93) * n^(n-1) / (2^(5/2) * log(31/27)^(n - 1/2) * exp(n)). - _Vaclav Kotesovec_, Nov 10 2023

%t Table[Sum[(3*k)!/(2*k+1)! * StirlingS2[n,k], {k,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, Nov 10 2023 *)

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

%Y Cf. A367155, A367158, A367164.

%Y Cf. A052895.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 07 2023