A392853 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 - log(1-x)^3) ).

1, 0, 0, 6, 36, 210, 3510, 62664, 1006152, 19759944, 479763000, 12430355256, 345693758256, 10718483051952, 363093592863456, 13153720329946944, 510677033417637120, 21246614370145152000, 940196323976050961280, 44044547616208359884160, 2180583631505389680967680

Offset

0,4

Links

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

Formula

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

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

Mathematica

Table[(1/(n+1))*Sum[(3*k)!*Binomial[n+1, k]*Abs[StirlingS1[n, 3*k]], {k, 0, Floor[n/3]}], {n, 0, 23}] (* Vincenzo Librandi, Jan 26 2026 *)

Prog

(PARI) a(n) = sum(k=0, n\3, (3*k)!*binomial(n+1, k)*abs(stirling(n, 3*k, 1)))/(n+1);
(Magma) [(1/(n+1))* &+[Factorial(3*k)*Binomial(n+1, k)*Abs(StirlingFirst(n, 3*k)): k in [0..Floor(n/3)] ] : n in [0..23] ]; // Vincenzo Librandi, Jan 26 2026

Crossrefs

Cf. A138013, A392852.

Cf. A392832, A392854.

Sequence in context: A353118 A357027 A357093 * A357029 A392763 A358859

Adjacent sequences: A392850 A392851 A392852 * A392854 A392855 A392856

Keyword

nonn

Author

Seiichi Manyama, Jan 25 2026

Status

approved