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%I #9 Mar 03 2022 06:10:59
%S 0,0,1,-6,35,-225,1624,-13132,118124,-1172700,12753576,-150917976,
%T 1931559552,-26596717056,392156797824,-6165817614720,102992244837120,
%U -1821602444624640,34012249593822720,-668609730341153280,13803759753640704000,-298631902863216384000
%N Stirling numbers of the first kind.
%C Coefficient of x^3 in Product {k=0..(n-1), x-k}.
%F E.g.f. (1+x)^(-1)*log(1+x)^2/2
%F a(n) = (-1)^n*det(S(i+3,j+2), 1 <= i,j <= n-2), where S(n,k) are Stirling numbers of the second kind and n>1. [_Mircea Merca_, Apr 06 2013]
%F a(n) ~ n! * (-1)^n * log(n)^2/2 * (1 + 2*gamma/log(n)), where gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Mar 03 2022
%t Table[StirlingS1[n, 3], {n, 1, 20}] (* _Vaclav Kotesovec_, Mar 03 2022 *)
%Y Cf. A000399, A008275, A081048.
%K easy,sign
%O 0,4
%A _Paul Barry_, Mar 05 2003
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