A392856 E.g.f. A(x) satisfies A(x) = 1/(1 - x*log(1-x*A(x)^2)^2).

1, 0, 0, 6, 24, 110, 4200, 64316, 827904, 23096664, 627297840, 14881613472, 463760352000, 16563331324800, 574283021317824, 22059664905840480, 951974706405381120, 42383329871826585600, 1993103500021060983552, 101494941959582537746176, 5429040979989656288240640

Offset

0,4

Links

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

Formula

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

Mathematica

Table[n!* Sum[(2*k)!*Binomial[2*n-k+1, k]/(2*n-k+1)*Abs[StirlingS1[n-k, 2*k]]/(n-k)!, {k, 0, Floor[n/3]}], {n, 0, 20}] (* Vincenzo Librandi, Feb 06 2026 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\3, (2*k)!*binomial(2*n-k+1, k)/(2*n-k+1)*abs(stirling(n-k, 2*k, 1))/(n-k)!);
(Magma) [Factorial(n) * &+[Factorial(2*k)* Binomial(2*n-k+1, k)/(2*n-k+1) * Abs(StirlingFirst(n - k, 2*k)) / Factorial(n - k): k in [0..Floor(n/3)]]: n in [0..25] ]; // Vincenzo Librandi, Feb 06 2026

Crossrefs

Cf. A392823, A392829.

Cf. A392762.

Sequence in context: A392830 A392829 A392760 * A187668 A273813 A293257

Adjacent sequences: A392853 A392854 A392855 * A392857 A392858 A392859

Keyword

nonn

Author

Seiichi Manyama, Jan 25 2026

Status

approved