A371005 Expansion of e.g.f. (1/x) * Series_Reversion( x/(2*exp(x) - 1) ).

1, 2, 10, 86, 1074, 17742, 366026, 9074102, 263006050, 8732015390, 326876957562, 13624410416454, 625859432308754, 31418430350730542, 1711378030988087338, 100535991279811936982, 6336275006902469756610, 426480351471985076800062

Offset

0,2

Links

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

Index entries for reversions of series

Formula

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

Crossrefs

Cf. A000272, A371006.

Sequence in context: A364396 A367372 A372177 * A208833 A145082 A335501

Adjacent sequences: A371002 A371003 A371004 * A371006 A371007 A371008

Keyword

nonn

Author

Seiichi Manyama, Mar 08 2024

Status

approved