OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..100
FORMULA
Sum_{n>=0} a(n)*x^n/n!^2 = BesselI(0,2*sqrt(x/(1-x)))/(1-x).
Recurrence: a(n)=(3*n^2-3*n+2)*a(n-1)-3*(n-1)^4*a(n-2)+(n-2)^3*(n-1)^3*a(n-3). - Vaclav Kotesovec, Sep 30 2012
a(n) ~ 1/sqrt(3)*n^(2*n+2/3)/exp(2*n-3*n^(1/3)). - Vaclav Kotesovec, Sep 30 2012
E.g.f.: exp(x) * Sum_{n>=0} x^n/n!^3 = Sum_{n>=0} a(n)*x^n/n!^3. - Paul D. Hanna, Nov 27 2012
MATHEMATICA
Table[Sum[(n!/k!)^2*Binomial[n, k], {k, 0, n}], {n, 0, 16}] (* Stefan Steinerberger, Jun 17 2007 *)
PROG
(PARI) a(n)=n!^3*polcoeff(exp(x+x*O(x^n))*sum(m=0, n, x^m/m!^3), n)
for(n=0, 25, print1(a(n), ", ")) \\ Paul D. Hanna, Nov 27 2012
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Jul 25 2006
EXTENSIONS
More terms from Stefan Steinerberger, Jun 17 2007
STATUS
approved