A375831 E.g.f. satisfies A(x) = exp(x * (exp(x^2*A(x)) - 1)).

1, 0, 0, 6, 0, 60, 1080, 840, 80640, 982800, 5292000, 249812640, 2854051200, 46711304640, 1595483809920, 22132648137600, 649972279756800, 19151306772998400, 377272414943424000, 14076577060273728000, 407012458114918656000, 11429334092933569612800

Offset

0,4

Links

Table of n, a(n) for n=0..21.

Formula

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

a(n) ~ sqrt((s + (2-r)*r^2*s^2) / (1 + r^2*s)) * n^(n-1) / (exp(n) * r^(n+1)), where r = 0.61449673663401194313060646272783564740280675129432866295196... and s = 2.0142668139632529702005737408942958028763507472726001354659... are real roots of the system of equations exp((-1 + exp(r^2*s))*r) = s, exp(r^2*s)*s*r^3 = 1. - Vaclav Kotesovec, Aug 31 2024

Mathematica

Table[n! * Sum[(k+1)^(n-2*k-1) * StirlingS2[k, n-2*k]/k!, {k, 0, Floor[n/2]}], {n, 0, 20}] (* Vaclav Kotesovec, Aug 31 2024 *)

Prog

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

Crossrefs

Cf. A349560, A375830.

Sequence in context: A191688 A375588 A375561 * A375830 A375833 A375832

Adjacent sequences: A375826 A375827 A375830 * A375832 A375833 A375834

Keyword

nonn,new

Author

Seiichi Manyama, Aug 30 2024

Status

approved