A392759 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - log(1-x)^2) ).

1, 0, 2, 6, 94, 940, 17348, 309708, 7306416, 184734576, 5473530432, 176925756480, 6380745801648, 249933477549600, 10665118139638272, 489943094795975520, 24179868161674982784, 1273841570260090509312, 71417817462566089624320, 4243564232503805507977728

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 - log(1-x*A(x))^2).

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

Mathematica

Table[(1/(n+1)!)*Sum[(2 k)!/k!*(n+k)!*Abs[StirlingS1[n, 2 k]], {k, 0, Floor[n/2]}], {n, 0, 19}] (* Vincenzo Librandi, Jan 23 2026 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-log(1-x)^2))/x))
(Magma) function a(n) s := 0; for k in [0..Floor(n/2)] do s +:= Factorial(2*k)/Factorial(k) * Factorial(n+k) * Abs(StirlingFirst(n, 2*k)); end for; return s / Factorial(n+1); end function;
[a(n) : n in [0..19]]; // Vincenzo Librandi, Jan 23 2026

Crossrefs

Cf. A392791, A392792, A392793.

Cf. A052802, A143154.

Sequence in context: A376408 A206156 A229052 * A363838 A280117 A129364

Adjacent sequences: A392756 A392757 A392758 * A392760 A392761 A392762

Keyword

nonn

Author

Seiichi Manyama, Jan 21 2026

Status

approved