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%I #13 Apr 23 2014 02:27:50
%S 1,2,13,180,4266,153180,7725510,519629040,44880355800,4835536256880,
%T 635221698211800,99872627051181600,18507444606249152400,
%U 3990439472567239692000,990119486841576670378800
%N a(n) = n!^2 times coefficient of x^n in e^(x*(3-x)/2/(1-x))/(1-x)^(1/2).
%D R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.65(b).
%H Vincenzo Librandi, <a href="/A073178/b073178.txt">Table of n, a(n) for n = 0..200</a>
%F e^(x*(3-x)/2/(1-x))/(1-x)^(1/2) = Sum_{n>=0} a(n)*x^n/n!^2. - _Vladeta Jovovic_, Aug 01 2006
%F a(n) ~ sqrt(Pi)*n^(2*n+1/2)*exp(2*sqrt(n)-2*n). - _Vaclav Kotesovec_, Apr 21 2014
%t CoefficientList[Series[E^(x*(3-x)/2/(1-x))/(1-x)^(1/2), {x, 0, 20}], x] * Range[0, 20]!^2 (* _Vaclav Kotesovec_, Apr 21 2014 *)
%o (PARI) a(n)=if(n<0,0,n!^2*polcoeff(exp(x*(3-x)/2/(1-x)+x*O(x^n))/sqrt(1-x+x*O(x^n)),n))
%Y Cf. A049088.
%K nonn
%O 0,2
%A _Michael Somos_, Jul 19 2002
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