A379884 E.g.f. A(x) satisfies A(x) = 1/(exp(-x*A(x)^2) - x).

1, 2, 15, 223, 5045, 154161, 5949715, 277816813, 15234148585, 959821848433, 68333878996991, 5425649143910733, 475370226250388221, 45559752911807595865, 4741534923025152367627, 532526268840445510805341, 64198018232238090097818065, 8268729272698380485865553761

Offset

0,2

Links

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

Formula

a(n) = n! * Sum_{k=0..n} (n+k+1)^(k-1) * binomial(n+k+1,n-k)/k!.

Prog

(PARI) a(n) = n!*sum(k=0, n, (n+k+1)^(k-1)*binomial(n+k+1, n-k)/k!);

Crossrefs

Cf. A377892, A379867.

Cf. A088690.

Sequence in context: A140054 A099085 A078365 * A207037 A218798 A176337

Adjacent sequences: A379879 A379880 A379882 * A379885 A379886 A379887

Keyword

nonn

Author

Seiichi Manyama, Jan 05 2025

Status

approved