A371116 E.g.f. satisfies A(x) = 1 + x^2*(exp(x*A(x)) - 1).

1, 0, 0, 6, 12, 20, 750, 7602, 47096, 589752, 11823930, 169812830, 2287327812, 46793930196, 1061518458182, 21163158296490, 458344052450160, 12165772611938672, 329982890581149426, 8764089834124752822, 255655700917556204540, 8220667673623130347020

Offset

0,4

Links

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

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} Stirling2(n-2*k,k)/(n-3*k+1)!.

Mathematica

nmax = 20; CoefficientList[Series[1 - x^2 - ProductLog[-E^(x*(1 - x^2))*x^3]/x, {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Mar 11 2024 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\3, stirling(n-2*k, k, 2)/(n-3*k+1)!);

Crossrefs

Cf. A000272, A371115.

Cf. A371118.

Sequence in context: A366564 A247212 A358013 * A356949 A375827 A362892

Adjacent sequences: A371113 A371114 A371115 * A371117 A371118 A371119

Keyword

nonn

Author

Seiichi Manyama, Mar 11 2024

Status

approved