login
A187646
(Signless) Central Stirling numbers of the first kind s(2n,n).
20
1, 1, 11, 225, 6769, 269325, 13339535, 790943153, 54631129553, 4308105301929, 381922055502195, 37600535086859745, 4070384057007569521, 480544558742733545125, 61445535102359115635655, 8459574446076318147830625, 1247677142707273537964543265, 196258640868140652967646352465
OFFSET
0,3
COMMENTS
Number of permutations with n cycles on a set of size 2n.
LINKS
FORMULA
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
MAPLE
seq(abs(Stirling1(2*n, n)), n=0..20);
MATHEMATICA
Table[Abs[StirlingS1[2n, n]], {n, 0, 12}]
N[1 + 1/(2 LambertW[-1, -Exp[-1/2]/2]), 50] (* The constant z in the asymptotic - Vladimir Reshetnikov, Oct 08 2016 *)
PROG
(Maxima) makelist(abs(stirling1(2*n, n)), n, 0, 12);
(PARI) for(n=0, 50, print1(abs(stirling(2*n, n, 1)), ", ")) \\ G. C. Greubel, Nov 09 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emanuele Munarini, Mar 12 2011
STATUS
approved