A371196 Expansion of e.g.f. 1/(1 + x * log(1 - x - x^2)).

1, 0, 2, 9, 56, 570, 5844, 75600, 1101568, 18059328, 330859440, 6657765840, 146394716544, 3488742148320, 89569620370944, 2464853317748640, 72368541315763200, 2258038571305305600, 74611690018599389184, 2602671162733649456640, 95577054989820127994880

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = n! * Sum_{j=0..n} Sum_{k=0..j} k! * binomial(j,n-j-k) * |Stirling1(j,k)|/j!.

Mathematica

With[{nn=20}, CoefficientList[Series[1/(1+x*Log[1-x-x^2]), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jun 04 2024 *)

Prog

(PARI) a(n) = n!*sum(j=0, n, sum(k=0, j, k!*binomial(j, n-j-k)*abs(stirling(j, k, 1))/j!));

Crossrefs

Cf. A331339, A371197, A371198.

Cf. A088369.

Sequence in context: A033917 A277482 A274393 * A004103 A295775 A223381

Adjacent sequences: A371193 A371194 A371195 * A371197 A371198 A371199

Keyword

nonn

Author

Seiichi Manyama, Mar 15 2024

Status

approved