OFFSET
0,3
FORMULA
G.f. satisfies: A(x) = Sum_{n>=0} x^n*Product_{k=1..n} (1 + x^k*A(x))/(1-x^k) due to the q-binomial theorem.
EXAMPLE
G.f.: A(x) = 1 + x + 3*x^2 + 6*x^3 + 14*x^4 + 31*x^5 + 72*x^6 + 166*x^7 +...
where the g.f. satisfies the identity:
A(x) = (1+x^2*A(x))/(1-x) * (1+x^3*A(x))/(1-x^2) * (1+x^4*A(x))/(1-x^3) *...
A(x) = 1 + x*(1+x*A(x))/(1-x) + x^2*(1+x*A(x))*(1+x^2*A(x))/((1-x)*(1-x^2)) + x^3*(1+x*A(x))*(1+x^2*A(x))*(1+x^3*A(x))/((1-x)*(1-x^2)*(1-x^3)) +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=prod(m=1, n, (1+x^(m+1)*A)/(1-x^m+x*O(x^n)))); polcoeff(A, n)}
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, x^m*prod(k=1, m, (1+x^k*A)/(1-x^k+x*O(x^n))))); polcoeff(A, n)}
for(n=0, 35, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 06 2012
STATUS
approved