A377425 E.g.f. satisfies A(x) = 1/(2 - exp(x*A(x)^2))^2.

1, 2, 24, 572, 20788, 1021892, 63498116, 4776128772, 422019084132, 42854861672612, 4918270207805188, 629575456637707076, 88938171122678982692, 13744507646644260776292, 2306659049841490720035780, 417774877069420589127228164, 81222489094387608969950071780

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A377424.

a(n) = (2/(4*n+2)!) * Sum_{k=0..n} (4*n+k+1)! * Stirling2(n,k).

a(n) ~ s^2 * n^(n-1) / (sqrt(2*r*s^2*(1 + 2*sqrt(s) + 4*r*s^(5/2)) - 1/2) * exp(n) * r^(n - 1/2)), where r = 0.0748939908815585832730777084358761067999141964960... and s = 1.51231153615975129726667843163402807258242679877... are roots of the system of equations s*(2 - exp(r*s^2))^2 = 1, 4*exp(r*s^2)*r*s^(5/2) = 1. - Vaclav Kotesovec, Feb 05 2026

Mathematica

Table[2/(4*n+2)! * Sum[(4*n+k+1)! * StirlingS2[n, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Feb 02 2026 *)

Prog

(PARI) a(n) = 2*sum(k=0, n, (4*n+k+1)!*stirling(n, k, 2))/(4*n+2)!;

Crossrefs

Cf. A367134, A376389.

Cf. A377424, A377428.

Sequence in context: A393751 A377490 A377492 * A170904 A090732 A377427

Adjacent sequences: A377422 A377423 A377424 * A377426 A377427 A377428

Keyword

nonn

Author

Seiichi Manyama, Oct 28 2024

Status

approved