A375721 Expansion of e.g.f. 1 / (1 + 3 * log(1 - x))^2.
1, 6, 60, 822, 14238, 297684, 7286076, 204251328, 6450932448, 226613038608, 8763294140064, 369900822475728, 16922169163019088, 833991953707934496, 44050579327333028448, 2482381132145285334912, 148660444826262311114880, 9427874254540824544312320
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+3*log(1-x))^2)) -
PARI
a(n) = sum(k=0, n, 3^k*(k+1)!*abs(stirling(n, k, 1)));
Formula
a(n) = Sum_{k=0..n} 3^k * (k+1)! * |Stirling1(n,k)|.
a(0) = 1; a(n) = 3 * Sum_{k=1..n} (k/n + 1) * (k-1)! * binomial(n,k) * a(n-k).
a(n) ~ sqrt(2*Pi) * n^(n + 3/2) / (9 * exp(2*n/3) * (exp(1/3) - 1)^(n+2)). - Vaclav Kotesovec, Sep 06 2024