A375722 Expansion of e.g.f. 1 / (1 + 3 * log(1 - x))^3.
1, 9, 117, 1962, 40122, 966276, 26755812, 836862192, 29167596504, 1120629465432, 47044646845848, 2142210019297680, 105154320625284240, 5534780654854980000, 310945503593770489440, 18570787974013838515200, 1174884522886771261079040
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))^3)) -
PARI
a(n) = sum(k=0, n, 3^k*(k+2)!*abs(stirling(n, k, 1)))/2;
Formula
a(n) = (1/2) * Sum_{k=0..n} 3^k * (k+2)! * |Stirling1(n,k)|.
a(0) = 1; a(n) = 3 * Sum_{k=1..n} (2*k/n + 1) * (k-1)! * binomial(n,k) * a(n-k).