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
Keywords
Programs
-
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);
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