A375722 - OEIS

%I #12 Aug 25 2024 09:56:09

%S 1,9,117,1962,40122,966276,26755812,836862192,29167596504,

%T 1120629465432,47044646845848,2142210019297680,105154320625284240,

%U 5534780654854980000,310945503593770489440,18570787974013838515200,1174884522886771261079040

%N Expansion of e.g.f. 1 / (1 + 3 * log(1 - x))^3.

%F a(n) = (1/2) * Sum_{k=0..n} 3^k * (k+2)! * |Stirling1(n,k)|.

%F a(0) = 1; a(n) = 3 * Sum_{k=1..n} (2*k/n + 1) * (k-1)! * binomial(n,k) * a(n-k).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+3*log(1-x))^3))

%o (PARI) a(n) = sum(k=0, n, 3^k*(k+2)!*abs(stirling(n, k, 1)))/2;

%Y Cf. A354263, A375721.

%Y Cf. A354122, A367475.

%Y Cf. A367473.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Aug 25 2024