A377646 - OEIS

%I #41 Nov 04 2024 09:15:22

%S 1,0,4,6,32,130,432,1274,3488,9090,22880,56122,134928,319202,745136,

%T 1719930,3931712,8912386,20053440,44825978,99614000,220200162,

%U 484441232,1061157946,2315254752,5033163650,10905189152,23555209914,50734299728,108984793570

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

%F a(n) = n! * Sum_{k=0..floor(n/2)} k! * binomial(2,k) * Stirling2(n-k,k)/(n-k)!.

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

%Y Cf. A377680, A377681.

%Y Cf. A375660.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Nov 04 2024