A392763 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 + log(1-x)^3) ).

1, 0, 0, 6, 36, 210, 4230, 77784, 1237992, 26654664, 704945160, 18827854056, 550132124256, 18354534720912, 658180365163776, 25065584828881344, 1033056038709198720, 45662370945463653120, 2136719060782029815040, 105947358954522743283840

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/(1 + log(1-x*A(x))^3).

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

Mathematica

Table[(1/(n+1)!)* Sum[(3*k)!/k!*(n+k)!*Abs[StirlingS1[n, 3*k]], {k, 0, Floor[n/3]}], {n, 0, 21}] (* Vincenzo Librandi, Feb 13 2026 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+log(1-x)^3))/x))
(Magma) [(1/Factorial(n+1)) * &+[Factorial(3*k) / Factorial(k) * Factorial(n+k)* Abs(StirlingFirst(n, 3*k)): k in [0..Floor(n/3)]]: n in [0..25] ]; // Vincenzo Librandi, Feb 13 2026

Crossrefs

Cf. A392720, A392759.

Sequence in context: A357093 A392853 A357029 * A358859 A357091 A268454

Adjacent sequences: A392760 A392761 A392762 * A392764 A392765 A392766

Keyword

nonn

Author

Seiichi Manyama, Jan 21 2026

Status

approved