A392930 E.g.f. A(x) satisfies A(x) = 1 - (A(x)/x) * log(1 - x^2*A(x)).

1, 1, 4, 33, 396, 6340, 127260, 3077340, 87148320, 2830355136, 103732886880, 4235797843200, 190719398802240, 9387982195637760, 501578338308727680, 28908756010609675200, 1787917373873184153600, 118111860756443012659200, 8300640816222360819333120, 618368718954996156764897280

Offset

0,3

Links

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

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (2*n-3*k)!/(n-k+1)! * |Stirling1(n-k,n-2*k)|/(n-k)!.

Mathematica

Table[n!* Sum[(2*n-3*k)!/(n-k+1)! *Abs[StirlingS1[n-k, n-2*k]]/(n-k)!, {k, 0, Floor[n/2]}], {n, 0, 20}] (* Vincenzo Librandi, Feb 03 2026 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\2, (2*n-3*k)!/(n-k+1)!*abs(stirling(n-k, n-2*k, 1))/(n-k)!);
(Magma) [Factorial(n)*&+[Factorial(2*n-3*k)/Factorial(n-k+1)* Abs(StirlingFirst(n-k, n-2*k)) / Factorial(n-k): k in [0..Floor(n/2)] ] : n in [0..24] ]; // Vincenzo Librandi, Feb 03 2026

Crossrefs

Cf. A392929, A392931.

Sequence in context: A295256 A269926 A392954 * A331794 A156132 A215364

Adjacent sequences: A392927 A392928 A392929 * A392931 A392932 A392933

Keyword

nonn

Author

Seiichi Manyama, Jan 27 2026

Status

approved