A390726 a(n) = (-1)^n*Stirling1(2*n, n)*(2*n)!/(n+1)!.

1, 1, 44, 6750, 2274384, 1357398000, 1267789406400, 1710145647690480, 3149899815315052800, 7600887375048946218240, 23277891409086910167936000, 88231498188018216186931776000, 405565255637303392039560631603200, 2223024959128781177959442293440000000, 14326217550468364573392121174440867840000

Offset

0,3

Comments

The central terms in the expansion of the Lambert W function in powers of log(log(x))/log(x), see A073315.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..190

Formula

a(n) = A073315(2*n, n).

a(n) = A187646(n)*A001761(n).

a(n) = n!*A390276(n).

Maple

A390726 := n -> (-1)^n*Stirling1(2*n, n)*(2*n)!/(n+1)!:
seq(A390726(n), n = 0..14);

Mathematica

Table[(-1)^n*StirlingS1[2 n, n]*Factorial[2 n]/Factorial[n+1], {n, 0, 15}] (* Vincenzo Librandi, Nov 19 2025 *)

Prog

(Magma) [(-1)^n*StirlingFirst(2*n, n)*Factorial(2*n)/Factorial(n+1): n in [0..20]]; // Vincenzo Librandi, Nov 19 2025

Crossrefs

Cf. A390276, A390727, A390277, A073315, A132393, A001761, A187646.

Sequence in context: A268548 A395206 A203974 * A266853 A323315 A007105

Adjacent sequences: A390723 A390724 A390725 * A390727 A390728 A390729

Keyword

nonn

Author

Peter Luschny, Nov 16 2025

Status

approved