A367879 - OEIS

%I #9 Dec 04 2023 06:37:05

%S 1,0,6,9,240,1170,25812,244440,5464512,79579584,1926411120,

%T 37900930320,1018338863616,25047229315680,752077828672128,

%U 22027545026192160,738063856107279360,24935406131189352960,927531711339595204608,35370336293213512527360

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

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

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

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

%Y Cf. A052830, A367878.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Dec 03 2023