OFFSET
0,3
FORMULA
a(n) = 1 - Sum_{k=0..n-1} a(k)*(-1)^(n-k)*C(k^2+k + n-k-1, n-k) for n>0, with a(0)=1.
EXAMPLE
1/(1-x) = 1 + x/(1+x)^2 + 3*x^2/(1+x)^6 + 16*x^3/(1+x)^12 + 134*x^4/(1+x)^20 +...
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*(m+1))), n))}
(PARI) {a(n)=if(n==0, 1, 1 - sum(j=0, n-1, a(j)*(-1)^(n-j)*binomial(j*(j+1)+n-j-1, n-j)))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 31 2010
STATUS
approved