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
Keywords
Programs
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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));
Formula
a(n) = 1/(3*(n+1)) * Sum_{k=0..n+1} 2^k * k^n * binomial(n+1,k).
a(n) = n! * Sum_{k=0..n} 2^k * 3^(n-k) * Stirling2(n,k)/(n-k+1)!. - Seiichi Manyama, Nov 07 2024