A367164 E.g.f. satisfies A(x) = 1 + A(x)^3 * (1 - exp(-x)).

1, 1, 5, 55, 929, 21271, 616265, 21624415, 891671009, 42263854471, 2264336600825, 135325966276975, 8926057815521489, 644116254555006871, 50477965058305364585, 4269330999037434100735, 387619447676360230226369, 37602089272441407334114471

Offset: 0

Author

Seiichi Manyama, Nov 07 2023

Keywords

• nonn

Crossrefs

Cf. A367155, A367158, A367161.

Cf. A006531.

Programs

Mathematica

Table[Sum[(-1)^(n-k) * (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, (-1)^(n-k)*(3*k)!/(2*k+1)!*stirling(n, k, 2));

Formula

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

a(n) ~ sqrt(69) * n^(n-1) / (2^(5/2) * log(27/23)^(n - 1/2) * exp(n)). - Vaclav Kotesovec, Nov 10 2023