A370907 Expansion of e.g.f. (1/x) * Series_Reversion( 3*x/(2 + exp(3*x)) ).

1, 1, 5, 42, 519, 8526, 175329, 4338594, 125632035, 4169652390, 156101072373, 6508965708378, 299190004799679, 15031796956994286, 819581031710623017, 48199003176462356754, 3041324249730311069595, 204962505644116505863926

Offset

0,3

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^(n+1-k) * k^n * binomial(n+1,k).

Prog

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

Crossrefs

Cf. A201595, A370908.

Sequence in context: A102693 A052654 A108398 * A239997 A102244 A323313

Adjacent sequences: A370904 A370905 A370906 * A370908 A370909 A370910

Keyword

nonn

Author

Seiichi Manyama, Mar 05 2024

Status

approved