|
%I #22 Jul 11 2023 08:04:17
%S 1,0,4,6,64,300,2568,20160,193856,1989792,22687200,279956160,
%T 3737966208,53589444480,821522026752,13407498599040,232106716968960,
%U 4248256958023680,81968803604600832,1662870215019018240,35384007384670648320,788053048823608565760
%N Expansion of e.g.f.: (1-x)^(-2x).
%D R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.3.
%H Vincenzo Librandi, <a href="/A053489/b053489.txt">Table of n, a(n) for n = 0..200</a>
%F E.g.f.: (1-x)^(-2*x).
%F a(n) = (-1)^n*Sum_{k=0..floor(n/2)} 2^k*binomial(n, k)*k!*Stirling1(n-k, k). - _Vladeta Jovovic_, Dec 19 2004
%F a(n) ~ n! * n * (1 + (1-2*log(n)-2*gamma)/n), where gamma is the Euler-Mascheroni constant (A001620). - _Vaclav Kotesovec_, Apr 21 2014
%t CoefficientList[Series[(1-x)^(-2*x), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Apr 21 2014 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace((1-x)^(-2*x))) \\ _G. C. Greubel_, Aug 29 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!((1-x)^(-2*x))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 29 2018
%Y Cf. A007113, A053490.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Jan 15 2000
|
