A355762 E.g.f. satisfies log(A(x)) = (exp(x*A(x)) - 1) * A(x)^2.

1, 1, 8, 125, 2987, 96727, 3963841, 196769897, 11480304448, 770031502467, 58386951857583, 4938864464154469, 461111056016847137, 47101341445053180079, 5225323162578044669492, 625646891309723527419137, 80416734865584980392853799, 11044230667889978466327860347

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = Sum_{k=0..n} (n+2*k+1)^(k-1) * Stirling2(n,k).

Prog

(PARI) a(n) = sum(k=0, n, (n+2*k+1)^(k-1)*stirling(n, k, 2));

Crossrefs

Cf. A030019, A349557.

Cf. A162656, A355763, A355766.

Sequence in context: A110272 A215040 A033536 * A215793 A273279 A227851

Adjacent sequences: A355759 A355760 A355761 * A355763 A355764 A355765

Keyword

nonn

Author

Seiichi Manyama, Jul 16 2022

Status

approved