A187646 - OEIS

%I #32 Jul 10 2023 07:48:00

%S 1,1,11,225,6769,269325,13339535,790943153,54631129553,4308105301929,

%T 381922055502195,37600535086859745,4070384057007569521,

%U 480544558742733545125,61445535102359115635655,8459574446076318147830625,1247677142707273537964543265,196258640868140652967646352465

%N (Signless) Central Stirling numbers of the first kind s(2n,n).

%C Number of permutations with n cycles on a set of size 2n.

%H Vincenzo Librandi, <a href="/A187646/b187646.txt">Table of n, a(n) for n = 0..200</a>

%F Asymptotic: a(n) ~ (2*n/(e*z*(1-z)))^n*sqrt((1-z)/(2*Pi*n*(2z-1))), where z=0.715331862959... is a root of the equation z = 2*(z-1)*log(1-z). - _Vaclav Kotesovec_, May 30 2011

%p seq(abs(Stirling1(2*n,n)), n=0..20);

%t Table[Abs[StirlingS1[2n, n]], {n, 0, 12}]

%t N[1 + 1/(2 LambertW[-1, -Exp[-1/2]/2]), 50] (* The constant z in the asymptotic - _Vladimir Reshetnikov_, Oct 08 2016 *)

%o (Maxima) makelist(abs(stirling1(2*n,n)),n,0,12);

%o (PARI) for(n=0,50, print1(abs(stirling(2*n, n, 1)), ", ")) \\ _G. C. Greubel_, Nov 09 2017

%Y Cf. A008275, A007820, A187235, A237993, A242676, A285862.

%K nonn,easy

%O 0,3

%A _Emanuele Munarini_, Mar 12 2011