A368165 Expansion of e.g.f. -log(1 + x^2/2 * log(1 - x)).

0, 0, 0, 3, 6, 20, 180, 1134, 7980, 78840, 798840, 8620920, 107668440, 1449377280, 20755871136, 323448048000, 5398086002400, 95487623038080, 1796842848654720, 35808112038746880, 751616958775939200, 16600116241063514880, 384905905873078867200

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..444

Formula

a(n) = n! * Sum_{k=1..floor(n/3)} (k-1)! * |Stirling1(n-2*k,k)|/(2^k * (n-2*k)!).

a(0) = a(1) = a(2) = 0; a(n) = n!/(2*(n-2)) + Sum_{k=3..n-1} k!/(2*(k-2)) * binomial(n-1,k) * a(n-k). - Seiichi Manyama, Jan 22 2025

Mathematica

With[{nn =30}, CoefficientList[Series[-Log[1+x^2/2 Log[1-x]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jan 22 2024 *)

Prog

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

Crossrefs

Cf. A052804, A368166.

Cf. A351505.

Sequence in context: A019042 A019052 A351492 * A351505 A355994 A375698

Adjacent sequences: A368162 A368163 A368164 * A368166 A368167 A368168

Keyword

nonn

Author

Seiichi Manyama, Dec 14 2023

Status

approved