A392832 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 - x^2*log(1-x)^3) ).

1, 0, 0, 0, 0, 120, 1080, 8820, 75600, 701568, 25235280, 736589040, 17454333600, 376218063936, 7825958011872, 207779505635520, 7160585771888640, 266170809822432768, 9680346223607877120, 339097779148341335040, 12234333214554427699200, 488121623700513688166400

Offset

0,6

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Formula

E.g.f. A(x) satisfies A(x) = 1 - (x*A(x))^2 * log(1-x*A(x))^3.

a(n) = (n!/(n+1)) * Sum_{k=0..floor(n/5)} (3*k)! * binomial(n+1,k) * |Stirling1(n-2*k,3*k)|/(n-2*k)!.

Mathematica

Table[(n!/(n+1))* Sum[(3*k)!*Binomial[n+1, k]*Abs[StirlingS1[n-2*k, 3*k]]/(n-2*k)!, {k, 0, Floor[n/5]}], {n, 0, 21}] (* Vincenzo Librandi, Feb 07 2026 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\5, (3*k)!*binomial(n+1, k)*abs(stirling(n-2*k, 3*k, 1))/(n-2*k)!)/(n+1);
(Magma) [(Factorial (n)/(n+1)) * &+[Factorial(3*k)* Binomial(n+1, k)* Abs(StirlingFirst(n - 2*k, 3*k)) / Factorial(n -2*k): k in [0..Floor(n/5)]]: n in [0..25] ]; // Vincenzo Librandi, Feb 07 2026

Crossrefs

Cf. A371138, A392831.

Cf. A392828.

Sequence in context: A052777 A392828 A052765 * A265091 A371107 A371051

Adjacent sequences: A392829 A392830 A392831 * A392833 A392834 A392835

Keyword

nonn

Author

Seiichi Manyama, Jan 24 2026

Status

approved