%I #19 Sep 08 2022 08:45:00
%S 1,0,6,9,132,630,6642,55440,608976,6790392,85413960,1145077560,
%T 16600386888,256806229680,4233767671728,74015194485960,
%U 1368023697469440,26649263762049600,545697922821501888,11717708270380421760,263276186128105633920
%N Expansion of e.g.f.: (1-x)^(-3x).
%D R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.3.
%H Vincenzo Librandi, <a href="/A053490/b053490.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = (-1)^n*Sum_{k=0..floor(n/2)} 3^k*binomial(n, k)*k!*Stirling1(n-k, k). - _Vladeta Jovovic_, Dec 19 2004
%F a(n) ~ n! * n^2/2 * (1 + (9-6*log(n)-6*gamma)/n), where gamma is the Euler-Mascheroni constant (A001620). - _Vaclav Kotesovec_, Apr 21 2014
%t CoefficientList[Series[(1-x)^(-3*x), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Apr 21 2014 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace((1-x)^(-3*x))) \\ _G. C. Greubel_, Aug 29 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!((1-x)^(-3*x))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 29 2018
%Y Cf. A007113, A053489.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Jan 15 2000