A376292 E.g.f. satisfies A(x) = 1 - (x*A(x))^3 * log(1 - x*A(x)).

1, 0, 0, 0, 24, 60, 240, 1260, 169344, 1693440, 17150400, 187941600, 12778698240, 271809457920, 5031211086720, 91848556800000, 4643532967772160, 154079136039628800, 4367731446302515200, 117143657916761548800, 5457792037686441984000

Offset

0,5

Links

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

Index entries for reversions of series

Formula

a(n) = (n!)^2 * Sum_{k=0..floor(n/4)} |Stirling1(n-3*k,k)|/( (n-3*k)! * (n-k+1)! ).

E.g.f.: (1/x) * Series_Reversion( x/(1 - x^3*log(1 - x)) ).

Mathematica

Table[(n!)^2*Sum[ Abs[StirlingS1[n-3*k, k]/((n-3*k)!*(n-k+1)!)], {k, 0, Floor[n/4]}], {n, 0, 23}] (* Vincenzo Librandi, Mar 02 2026 *)

Prog

(PARI) a(n) = n!^2*sum(k=0, n\4, abs(stirling(n-3*k, k, 1))/((n-3*k)!*(n-k+1)!));
(Magma) [(Factorial(n))^2* &+[Abs(StirlingFirst(n-3*k, k)) /( Factorial(n-3*k) * Factorial(n-k+1) ): k in [0..Floor(n/4)] ] : n in [0..23] ]; // Vincenzo Librandi, Mar 02 2026

Crossrefs

Cf. A138013, A371121, A371138.

Sequence in context: A356099 A391377 A356971 * A370995 A226883 A304547

Adjacent sequences: A376289 A376290 A376291 * A376293 A376294 A376295

Keyword

nonn

Author

Seiichi Manyama, Sep 19 2024

Status

approved