A357394 E.g.f. satisfies A(x) = exp(x * exp(2 * A(x))) - 1.

0, 1, 5, 55, 953, 22651, 685525, 25222359, 1093148145, 54549313651, 3080446982221, 194213549023407, 13522789698386281, 1030619149263349387, 85336828127587240261, 7628421633465044832391, 732208108150442899232737, 75108533335473988089786147

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = Sum_{k=1..n} (2 * n)^(k-1) * Stirling2(n,k).

a(n) ~ n^(n-1) / (2 * sqrt(1 + LambertW(1/2)) * LambertW(1/2)^n * exp(n*(3 - 1/LambertW(1/2)))). - Vaclav Kotesovec, Nov 14 2022

Mathematica

Table[Sum[(2*n)^(k-1) * StirlingS2[n, k], {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 14 2022 *)

Prog

(PARI) a(n) = sum(k=1, n, (2*n)^(k-1)*stirling(n, k, 2));

Crossrefs

Cf. A052888, A357395.

Cf. A357335.

Sequence in context: A008543 A057130 A141357 * A093352 A293013 A195513

Adjacent sequences: A357391 A357392 A357393 * A357395 A357396 A357397

Keyword

nonn

Author

Seiichi Manyama, Sep 26 2022

Status

approved