A367158 E.g.f. satisfies A(x) = 1 - A(x)^3 * log(1 - x).

1, 1, 7, 92, 1824, 48804, 1649724, 67492872, 3243567552, 179139978072, 11181615816216, 778466939121552, 59811143359463952, 5027200928936108064, 458865351655379262432, 45201262487568977507328, 4779609140451030860102400, 539990133396500652971120640

Offset: 0

Author

Seiichi Manyama, Nov 07 2023

Keywords

• nonn

Crossrefs

Cf. A367155, A367161, A367164.

Cf. A052803.

Programs

Mathematica

Table[Sum[(-1)^(n-k) * (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)!*abs(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(23*n/27) * (exp(4/27) - 1)^(n - 1/2)). - Vaclav Kotesovec, Nov 10 2023