A377892 E.g.f. A(x) satisfies A(x) = (1 + x*A(x)^2) * exp(x * A(x)^2).

1, 2, 19, 352, 9885, 374486, 17907991, 1035748260, 70334590969, 5487022612810, 483655093883451, 47541690024105608, 5156503816883562325, 611769291578643110238, 78812382009451814165695, 10956572374811382997014796, 1634950184384280878142249969, 260653481562714033459279871250

Offset

0,2

Links

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

Formula

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

a(n) ~ sqrt(5/sqrt(17)-1) * 2^(3*n+1) * exp((2*(sqrt(17)-5)*n + sqrt(17)-3)/4) * n^(n-1) / (3*sqrt(17)-11)^(n+1). - Vaclav Kotesovec, Jan 31 2026

Mathematica

Table[n! * Sum[(2*n+1)^(k-1) * Binomial[2*n+1, n-k]/k!, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jan 31 2026 *)

Prog

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

Crossrefs

Cf. A088690, A377893.

Sequence in context: A187659 A387000 A308330 * A078369 A380768 A090308

Adjacent sequences: A377889 A377890 A377891 * A377893 A377894 A377895

Keyword

nonn

Author

Seiichi Manyama, Nov 11 2024

Status

approved