OFFSET
0,2
COMMENTS
An example of this logarithmic identity at q=2:
Sum_{n>=1} [q^(n^2)/(1 - q^n*x)^n]*x^n/n = Sum_{n>=1} [(1 + q^n)^n - 1]*x^n/n.
FORMULA
G.f.: A(x) = (1-x)*exp( Sum_{n>=1} (1 + 2^n)^n * x^n/n );
Equals the first differences of A155201.
EXAMPLE
G.f.: A(x) = 1 + 2*x + 14*x^2 + 268*x^3 + 21462*x^4 +...
log(A(x)) = 2/(1-2*x)*x + 2^4/(1-2^2*x)^2*x^2/2 + 2^9/(1-2^3*x)^3*x^3/3 +...
log(A(x)) = (3-1)*x + (5^2-1)*x^2/2 + (9^3-1)*x^3/3 + (17^4-1)*x^4/4 +...
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, 2^(m^2)/(1-2^m*x)^m*x^m/m)+x*O(x^n)), n)}
(PARI) /* As First Differences of A155201: */
{a(n)=polcoeff((1-x)*exp(sum(m=1, n+1, (2^m+1)^m*x^m/m)+x*O(x^n)), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 17 2009
STATUS
approved