A355788 E.g.f. satisfies log(A(x)) = (exp(2*x) - 1) * A(x)/2.

1, 1, 5, 38, 409, 5772, 101227, 2126966, 52153185, 1462998168, 46232500275, 1625693415898, 62972266884721, 2664713395180228, 122315552809623323, 6053803331878334590, 321389617069279569345, 18218906261462603910704, 1098415656103838009681123

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

E.g.f.: exp( -LambertW((1 - exp(2*x))/2) ).

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

From Vaclav Kotesovec, Jul 18 2022: (Start)

E.g.f.: 2*LambertW((1 - exp(2*x))/2) / (1 - exp(2*x)).

a(n) ~ 2^(n - 1/2) * sqrt(exp(1) + 2) * n^(n-1) / (exp(n-1) * (log(exp(1) + 2) - 1)^(n - 1/2)). (End)

Prog

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

Crossrefs

Cf. A052880, A355781.

Sequence in context: A217701 A371342 A069471 * A216858 A338867 A110467

Adjacent sequences: A355785 A355786 A355787 * A355789 A355790 A355791

Keyword

nonn

Author

Seiichi Manyama, Jul 17 2022

Status

approved