A370909 Expansion of e.g.f. (1/x) * Series_Reversion( 3*x/(1 + 2*exp(3*x)) ).

1, 2, 14, 174, 3174, 76902, 2331630, 85048686, 3629630070, 177523551990, 9793095667326, 601667773414974, 40747538527887366, 3016185673617546822, 242280567558408368142, 20991011860150103490318, 1951271511259385883645846, 193723174296061459833879702

Offset

0,2

Links

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

Index entries for reversions of series

Formula

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

Prog

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

Crossrefs

Cf. A201595, A370910.

Sequence in context: A308449 A233224 A167014 * A366736 A300282 A336635

Adjacent sequences: A370906 A370907 A370908 * A370910 A370911 A370912

Keyword

nonn

Author

Seiichi Manyama, Mar 05 2024

Status

approved