A392938 E.g.f. A(x) satisfies A(x) = 1 - x*A(x) * log(1 - x^3*A(x)^3).

1, 0, 0, 0, 24, 0, 0, 2520, 161280, 0, 1209600, 219542400, 10538035200, 1556755200, 559394035200, 68652904320000, 2933375142297600, 2519452615680000, 571411853236224000, 58957325331480576000, 2375999133429841920000, 6705686160036864000000, 1226258032083280035840000

Offset

0,5

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^3)) ).

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

Mathematica

Table[(n!)^2* Sum[1/(3*k+1)!*Abs[StirlingS1[k, n-3*k]]/k!, {k, 0, Floor[n/3]}], {n, 0, 20}] (* Vincenzo Librandi, Feb 04 2026 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(1-x*log(1-x^3)))/x))
(Magma) [Factorial(n)^2*&+[1/Factorial(3*k+1)* Abs(StirlingFirst(k, n-3*k))/Factorial(k): k in [0..Floor(n/3)] ] : n in [0..24] ]; // Vincenzo Librandi, Feb 04 2026

Crossrefs

Cf. A371121, A392933.

Sequence in context: A375589 A375562 A392996 * A376347 A376346 A392892

Adjacent sequences: A392935 A392936 A392937 * A392939 A392940 A392941

Keyword

nonn

Author

Seiichi Manyama, Jan 27 2026

Status

approved