A377646 Expansion of e.g.f. (1 + x * (exp(x) - 1))^2.

1, 0, 4, 6, 32, 130, 432, 1274, 3488, 9090, 22880, 56122, 134928, 319202, 745136, 1719930, 3931712, 8912386, 20053440, 44825978, 99614000, 220200162, 484441232, 1061157946, 2315254752, 5033163650, 10905189152, 23555209914, 50734299728, 108984793570

Offset

0,3

Links

Table of n, a(n) for n=0..29.

Formula

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

Prog

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

Crossrefs

Cf. A377680, A377681.

Cf. A375660.

Sequence in context: A239224 A087299 A229712 * A331513 A164127 A180139

Adjacent sequences: A377641 A377644 A377645 * A377647 A377648 A377649

Keyword

nonn,easy,new

Author

Seiichi Manyama, Nov 04 2024

Status

approved