A367878 Expansion of e.g.f. 1/(1 + 2 * x * log(1-x)).

1, 0, 4, 6, 112, 540, 8688, 78960, 1343872, 18162144, 346968000, 6157134720, 134058110976, 2912224423680, 72152130903552, 1839996238429440, 51471401675489280, 1500206702407741440, 46934038380170391552, 1535198134749947965440

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(0) = 1; a(n) = 2 * n! * Sum_{k=2..n} 1/(k-1) * a(n-k)/(n-k)!.

a(n) = n! * Sum_{k=0..floor(n/2)} 2^k * k! * |Stirling1(n-k,k)|/(n-k)!.

Prog

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

Crossrefs

Cf. A052830, A367879.

Cf. A367883.

Sequence in context: A013023 A012909 A219507 * A012934 A013165 A337466

Adjacent sequences: A367875 A367876 A367877 * A367879 A367880 A367881

Keyword

nonn

Author

Seiichi Manyama, Dec 03 2023

Status

approved