A351274 a(0) = 1; thereafter a(n) = Sum_{k=1..n} (2*k)^k * Stirling1(n,k).

1, 2, 14, 172, 2964, 65848, 1789688, 57521280, 2133964352, 89744964288, 4219022123328, 219246630903936, 12479659844383104, 772174659456713472, 51603153976362554112, 3704166182571098222592, 284239227254465994240000, 23218955083323248158556160

Offset

0,2

Links

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

Eric Weisstein's World of Mathematics, Lambert W-Function.

Formula

E.g.f.: 1/(1 + LambertW( -2 * log(1+x) )), where LambertW() is the Lambert W-function.

a(n) ~ n^n / (sqrt(2) * (exp(exp(-1)/2) - 1)^(n+1/2) * exp(n - exp(-1)/4 + 1/2)). - Vaclav Kotesovec, Feb 06 2022

Mathematica

Join[{1}, Table[Sum[(2k)^k StirlingS1[n, k], {k, n}], {n, 20}]] (* Harvey P. Dale, Dec 31 2023 *)

Prog

(PARI) a(n) = sum(k=0, n, (2*k)^k*stirling(n, k, 1));
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+lambertw(-2*log(1+x)))))

Crossrefs

Cf. A305819, A351182, A351275, A351276.

Sequence in context: A141012 A351277 A235369 * A228476 A308449 A233224

Adjacent sequences: A351271 A351272 A351273 * A351275 A351276 A351277

Keyword

nonn

Author

Seiichi Manyama, Feb 05 2022

Extensions

Made a(0) = 1 explicit and changed range of k in definition to start at 1 at the suggestion of Harvey P. Dale. - N. J. A. Sloane, Dec 31 2023

Status

approved