A380718 E.g.f. A(x) satisfies A(x) = exp(x * A(x)^2) / (1 - x*A(x)).

1, 2, 17, 277, 6809, 225381, 9408745, 474835159, 28128322801, 1913917635433, 147124118481641, 12610993501595523, 1192699876840875529, 123380247466574450509, 13858619936380747514953, 1679795510876270598645631, 218541202774350975212752865, 30376105717226232363041309265

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(2*n,n-k)/k!.

Prog

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

Crossrefs

Cf. A380663, A380719.

Cf. A377831.

Sequence in context: A338635 A268705 A380771 * A078367 A377888 A090306

Adjacent sequences: A380708 A380716 A380717 * A380719 A380720 A380721

Keyword

nonn,new

Author

Seiichi Manyama, Jan 30 2025

Status

approved