A392933 E.g.f. A(x) satisfies A(x) = 1 - x*A(x) * log(1 - x^2*A(x)^2).

1, 0, 0, 6, 0, 60, 2160, 1680, 161280, 4445280, 16632000, 1105695360, 28740096000, 284367283200, 16330915560960, 442998043488000, 8416540945612800, 454486527394099200, 13751235468556185600, 406476934064583782400, 21668282110429194240000, 759789627140273393664000

Offset

0,4

Links

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

Formula

E.g.f.: (1/x) * Series_Reversion( x/(1 - x*log(1-x^2)) ).

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

Mathematica

Table[(n!)^2 * Sum[1/(2*k+1)!*Abs[StirlingS1[k, n-2*k]/k!], {k, 0, Floor[n/2]}], {n, 0, 20}] (* Vincenzo Librandi, Jan 28 2026 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(1-x*log(1-x^2)))/x))
(Magma) [Factorial((n))^2* &+[1/Factorial(2*k+1) * Abs(StirlingFirst(k, n-2*k))/Factorial(k): k in [0..Floor(n/2)] ] : n in [0..23] ]; // Vincenzo Librandi, Jan 28 2026

Crossrefs

Cf. A376344, A392934.

Cf. A371121, A392938.

Sequence in context: A392955 A392957 A392931 * A376351 A376350 A376345

Adjacent sequences: A392930 A392931 A392932 * A392934 A392935 A392936

Keyword

nonn

Author

Seiichi Manyama, Jan 27 2026

Status

approved