OFFSET
0,3
COMMENTS
Triangle A008459 consists of squared binomial coefficients.
FORMULA
a(n) = 1 + (1/n)*Sum_{k=0..n-1} C(n, k)^2*k*a(k) for n>0, with a(0)=0.
Sum_{n>=0} a(n)*x^n/n!^2 = -log(2-BesselI(0,2*sqrt(x))). - Vladeta Jovovic, Jul 16 2006
EXAMPLE
a(2) = 3 = 1 + (1*0*0 + 4*1*1)/2,
a(3) = 22 = 1 + (1*0*0 + 9*1*1 + 9*2*3)/3,
a(4) = 323 = 1 + (1*0*0 + 16*1*1 + 36*2*3 + 16*3*22)/4,
a(5) = 7906 = 1 + (1*0*0 + 25*1*1 + 100*2*3 + 100*3*22 + 25*4*323)/5.
PROG
(PARI) a(n)=if(n<1, 0, 1+sum(k=0, n-1, binomial(n, k)^2*k*a(k))/n)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 31 2004
STATUS
approved