A187646 (Signless) Central Stirling numbers of the first kind s(2n,n).

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

Vincenzo Librandi, Table of n, a(n) for n = 0..200

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

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

Sequence in context: A089917 A294388 A281257 * A347482 A170948 A245076

Adjacent sequences: A187643 A187644 A187645 * A187647 A187648 A187649

Keyword

nonn,easy

Author

Emanuele Munarini, Mar 12 2011

Status

approved