A371008 Expansion of e.g.f. (1/x) * Series_Reversion( x/(3 - 2*exp(x)) ).

1, -2, 6, -14, -82, 2058, -22778, 55186, 4737630, -141417830, 1940770358, 18532189410, -2031211536242, 63333969461098, -624072759994266, -46503997775007182, 3129486110236404926, -90436659990999596742, -559947921342589721450

Offset

0,2

Links

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

Index entries for reversions of series

Formula

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

a(n) = n! * Sum_{k=0..n} (-2)^k * Stirling2(n,k)/(n-k+1)!. - Seiichi Manyama, Nov 07 2024

Prog

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

Crossrefs

Cf. A371009.

Sequence in context: A192764 A055691 A072171 * A308568 A296054 A333121

Adjacent sequences: A371005 A371006 A371007 * A371009 A371010 A371011

Keyword

sign

Author

Seiichi Manyama, Mar 08 2024

Status

approved