OFFSET
0,3
FORMULA
a(n) = 1 - Sum_{k=0..n-1} a(k)*(-1)^(n-k)*C(k(3k-1)/2 + n-k-1, n-k) for n>0, with a(0)=1.
EXAMPLE
1/(1-x) = 1 + x/(1+x) + 2*x^2/(1+x)^5 + 10*x^3/(1+x)^12 + 92*x^4/(1+x)^22 + 1314*x^5/(1+x)^35 + 26216*x^6/(1+x)^51 +...
PROG
(PARI) {a(n)=if(n==0, 1, polcoeff(-(1-x)*sum(m=0, n-1, a(m)*x^m/(1+x +x*O(x^n))^(m*(3*m-1)/2)), n))}
(PARI) {a(n)=if(n==0, 1, 1 - sum(j=0, n-1, a(j)*(-1)^(n-j)*binomial(j*(3*j-1)/2+n-j-1, n-j)))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 31 2010
STATUS
approved