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
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
Programs
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Maple
seq(abs(Stirling1(2*n,n)), n=0..20);
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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 *) -
Maxima
makelist(abs(stirling1(2*n,n)),n,0,12);
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PARI
for(n=0,50, print1(abs(stirling(2*n, n, 1)), ", ")) \\ G. C. Greubel, Nov 09 2017
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
Equivalent: a(n) ~ n!*(2*r^2/(r-1))^n/(2*Pi*n*sqrt(r-2)), where r=A226278. - Natalia L. Skirrow, Jul 13 2025
From Seiichi Manyama, May 20 2025: (Start)
a(n) = A132393(2*n,n).
a(n) = (2*n)! * [x^(2*n)] (-log(1 - x))^n / n!. (End)
Comments