OFFSET
0,2
COMMENTS
Limit a(n+1)/a(n) ~ 3.3829757679..., real root of cubic (1+x+3*x^2-x^3).
FORMULA
Empirical G.f.: (x^3+x^2+x-1)*(2*x^5+5*x^4-4*x^3+10*x^2-6*x+1) / ((x-1)^2*(x^2+2*x-1)^2*(x^3+x^2+3*x-1)). [Colin Barker, Nov 21 2012]
PROG
(PARI) {a(n)=if(n<0, 0, if(n==0, 1, sum(k=0, n, sum(j=0, k, binomial(n-j, k-j)* (binomial(2*(n-k), 2*j)-2*j*(n-k-j)*binomial(n-k, j)/if(n==k+1, 1, (n-k-1)))))))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 10 2005
STATUS
approved