A377890 E.g.f. A(x) satisfies A(x) = (1 + x*A(x)^2) * exp(x * A(x)).

1, 2, 15, 211, 4433, 124741, 4412815, 188335981, 9421966209, 540884623753, 35054089163351, 2531882857204273, 201689970517618225, 17567711167993834381, 1661084543502646535967, 169448367505003640681221, 18550123929621138841581185, 2169272360350263071212545553

Offset

0,2

Links

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

Formula

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

E.g.f.: (1/x) * Series_Reversion( x * (exp(-x) - x) ). - Seiichi Manyama, Dec 29 2024

Prog

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

Crossrefs

Cf. A088690, A377826, A377891.

Sequence in context: A143881 A380762 A380663 * A298692 A361617 A132493

Adjacent sequences: A377887 A377888 A377889 * A377891 A377892 A377893

Keyword

nonn

Author

Seiichi Manyama, Nov 11 2024

Status

approved