A392765 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - (exp(x)-1)^2) ).

1, 0, 2, 6, 86, 870, 14942, 264726, 5933174, 146722470, 4174735982, 131077743126, 4560210165062, 173031374724390, 7134885213734462, 317190775386859926, 15136241602198757270, 771407543960187434790, 41827159120486727660942, 2404019686442874374551446

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

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

Mathematica

Table[(1/(n+1)!)* Sum[(2*k)!/k!*(n+k)!*StirlingS2[n, 2*k], {k, 0, Floor[n/2]}], {n, 0, 21}] (* Vincenzo Librandi, Feb 13 2026 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-(exp(x)-1)^2))/x))
(Magma) [(1/Factorial(n+1)) * &+[Factorial(2*k) / Factorial(k) * Factorial(n+k)* StirlingSecond(n, 2*k): k in [0..Floor(n/2)]]: n in [0..25] ]; // Vincenzo Librandi, Feb 13 2026

Crossrefs

Cf. A052894.

Sequence in context: A118537 A109892 A268534 * A055702 A364794 A334779

Adjacent sequences: A392762 A392763 A392764 * A392766 A392767 A392768

Keyword

nonn

Author

Seiichi Manyama, Jan 22 2026

Status

approved