OFFSET
0,3
FORMULA
G.f.: 1 + x*(1 - G(0))/(1-x) where G(k) = 1 - 1/(1-x^(k+1))^(k+1)/(1-x/(x-1/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 23 2013
EXAMPLE
G.f.: A(x) = 1 + x + 2*x^2 + 3*x^3 + 6*x^4 + 9*x^5 + 18*x^6 + 27*x^7 +...
where
A(x) = 1 + x/(1-x) + x^2/((1-x)*(1-x^2)^2) + x^3/((1-x)*(1-x^2)^2*(1-x^3)^3) + x^4/((1-x)*(1-x^2)^2*(1-x^3)^3*(1-x^4)^4) +...
PROG
(PARI) {a(n)=polcoeff(sum(m=0, n, x^m/prod(k=1, m, (1-x^k +x*O(x^n))^k)), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 03 2012
STATUS
approved