A073179 a(n) = n!^2 times coefficient of x^n in Sum_{k>=0} x^k/k!^2/4^k*((2-x)/(1-x))^(2*k).

1, 1, 5, 64, 1417, 47801, 2278981, 145735360, 12026529089, 1243307884537, 157278532956301, 23885127975415136, 4286460830620175065, 897058398619374567889, 216462065577670278012557

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[BesselI[0,(2-x)/(1-x)*Sqrt[x]], {x, 0, 20}], x] * Range[0, 20]!^2 (* Vaclav Kotesovec, Apr 21 2014 *)

PARI

{a(n)=if(n<0, 0, n!^2*polcoeff(sum(k=0, n, x^k/k!^2/4^k* ((2-x)/(1-x))^(2*k), x*O(x^n)), n))}

Formula

Sum_{k>=0} x^k/k!^2/4^k*((2-x)/(1-x))^(2*k) = Sum_{n>=0} a(n)*x^n/n!^2. - Vladeta Jovovic, Aug 01 2006

BesselI(0,(2-x)/(1-x)*sqrt(x)) = Sum_{n>=0} a(n)*x^n/n!^2. - Vladeta Jovovic, Jun 20 2007