A371198 - OEIS

%I #7 Mar 15 2024 07:24:14

%S 1,0,0,0,24,180,960,8820,129024,2177280,32875200,533887200,9997827840,

%T 212133841920,4799669696640,114208231737600,2901190960926720,

%U 79007705121945600,2289453730357248000,69972073047194572800,2249392810263651532800

%N Expansion of e.g.f. 1/(1 + x^3 * log(1 - x - x^2)).

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

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

%Y Cf. A371196, A371197.

%Y Cf. A371158.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Mar 15 2024