A371007 Expansion of e.g.f. (1/x) * Series_Reversion( 2*x/(3*exp(2*x) - 1) ).

1, 3, 24, 336, 6864, 185808, 6286560, 255703584, 12163234560, 662866302720, 40735968170496, 2787616114300416, 210253334027606016, 17331011952028981248, 1550159522438672412672, 149539908497083261980672, 15476976326308703371984896

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Index entries for reversions of series

Formula

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

a(n) = n! * Sum_{k=0..n} 3^k * 2^(n-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(2*x/(3*exp(2*x)-1))/x))
(PARI) a(n) = sum(k=0, n+1, 3^k*(-1)^(n+1-k)*k^n*binomial(n+1, k))/(2*(n+1));

Crossrefs

Cf. A371005.

Sequence in context: A082166 A354259 A370055 * A144003 A334775 A153389

Adjacent sequences: A371004 A371005 A371006 * A371008 A371009 A371010

Keyword

nonn

Author

Seiichi Manyama, Mar 08 2024

Status

approved