A392789 Expansion of e.g.f. (1/x) * Series_Reversion( x + (1 - exp(x^3))/x ).

1, 1, 4, 30, 348, 5460, 108000, 2578800, 72189600, 2319166080, 84119968800, 3400710112800, 151635740256000, 7393393739571840, 391334037586652160, 22347717728195059200, 1369596926501682278400, 89664110210432082124800, 6245228229359073860505600

Offset

0,3

Links

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

Formula

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

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (2*n-3*k)! * Stirling2(n-2*k,n-3*k)/(n-2*k)!.

Mathematica

Table[(1/(n+1))*Sum[(2*n-3*k)!*Abs[StirlingS2[n-2*k, n-3*k]/(n-2*k)!], {k, 0, Floor[n/3]}], {n, 0, 21}] (* Vincenzo Librandi, Jan 24 2026 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x+(1-exp(x^3))/x)/x))
(Magma) [ 1/(n+1)* &+[ Factorial(2*n-3*k)*StirlingSecond(n-2*k, n-3*k)/Factorial(n-2*k) : k in [0..Floor(n/3)] ] : n in [0..18] ]; // Vincenzo Librandi, Jan 24 2026

Crossrefs

Cf. A052894, A392788, A392790.

Sequence in context: A379936 A089918 A391472 * A392784 A371041 A132622

Adjacent sequences: A392786 A392787 A392788 * A392790 A392791 A392792

Keyword

nonn

Author

Seiichi Manyama, Jan 22 2026

Status

approved