OFFSET
0,3
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
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
MATHEMATICA
CoefficientList[Series[BesselI[0, (2-x)/(1-x)*Sqrt[x]], {x, 0, 20}], x] * Range[0, 20]!^2 (* Vaclav Kotesovec, Apr 21 2014 *)
PROG
(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))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Jul 19 2002
STATUS
approved