A390726 - OEIS

%I #13 Nov 19 2025 03:42:24

%S 1,1,44,6750,2274384,1357398000,1267789406400,1710145647690480,

%T 3149899815315052800,7600887375048946218240,

%U 23277891409086910167936000,88231498188018216186931776000,405565255637303392039560631603200,2223024959128781177959442293440000000,14326217550468364573392121174440867840000

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

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

%H Vincenzo Librandi, <a href="/A390726/b390726.txt">Table of n, a(n) for n = 0..190</a>

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

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

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

%p A390726 := n -> (-1)^n*Stirling1(2*n, n)*(2*n)!/(n+1)!:

%p seq(A390726(n), n = 0..14);

%t Table[(-1)^n*StirlingS1[2 n,n]*Factorial[2 n]/Factorial[n+1],{n,0,15}] (* _Vincenzo Librandi_, Nov 19 2025 *)

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

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

%K nonn

%O 0,3

%A _Peter Luschny_, Nov 16 2025