OFFSET
0,3
COMMENTS
More generally, for integers p and q, exp( Sum_{n>=1} (p^n - q^n)^n * x^n/n ) is a power series in x with integer coefficients.
EXAMPLE
G.f.: A(x) = 1 + x + 13*x^2 + 2299*x^3 + 4465027*x^4 + 83649932869*x^5 +...
where
log(A(x)) = (3-2)*x + (3^2 - 2^2)^2*x^2/2 + (3^3 - 2^3)^3*x^3/3 + (3^4 - 2^4)^4*x^4/4 + (3^5 - 2^5)^5*x^5/5 +...
more explicitly,
log(A(x)) = x + 5^2*x^2/2 + 19^3*x^3/3 + 65^4*x^4/4 + 211^5*x^5/5 +...
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n, (3^m-2^m)^m*x^m/m)+x*O(x^n)), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 20 2011
STATUS
approved