A370894 Expansion of e.g.f. (1/x) * Series_Reversion( x*(3 - exp(2*x))/2 ).

1, 1, 6, 64, 1016, 21576, 575680, 18525088, 698625408, 30229271680, 1476535180544, 80371762466304, 4824793854177280, 316685993746640896, 22563822118152880128, 1734427247284290015232, 143072322233503079038976, 12606854482934004152303616

Offset

0,3

Links

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

Formula

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

a(n) ~ 2^(2*n+1) * LambertW(3*exp(1))^(n+1) * n^(n-1) / (sqrt(1 + LambertW(3*exp(1))) * 3^(n+1) * exp(n) * (LambertW(3*exp(1)) - 1)^(2*n+1)). - Vaclav Kotesovec, Mar 06 2024

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(3-exp(2*x))/2)/x))
(PARI) a(n) = sum(k=0, n, 2^(n-k)*(n+k)!*stirling(n, k, 2))/(n+1)!;

Crossrefs

Cf. A052894, A370934.

Cf. A258922.

Sequence in context: A141008 A336114 A354494 * A258425 A365054 A249592

Adjacent sequences: A370891 A370892 A370893 * A370895 A370896 A370897

Keyword

nonn

Author

Seiichi Manyama, Mar 06 2024

Status

approved