A073178 a(n) = n!^2 times coefficient of x^n in e^(x*(3-x)/2/(1-x))/(1-x)^(1/2).

1, 2, 13, 180, 4266, 153180, 7725510, 519629040, 44880355800, 4835536256880, 635221698211800, 99872627051181600, 18507444606249152400, 3990439472567239692000, 990119486841576670378800

Offset: 0

Author

Michael Somos, Jul 19 2002

Keywords

• nonn

References

• R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.65(b).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A049088.

Programs

Mathematica

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 *)

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))

Formula

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

a(n) ~ sqrt(Pi)*n^(2*n+1/2)*exp(2*sqrt(n)-2*n). - Vaclav Kotesovec, Apr 21 2014