OFFSET
0,2
COMMENTS
More generally, it appears that for m integer, exp( Sum_{n>=1} (m^n + y)^n * x^n/n ) is a power series in x and y with integer coefficients.
FORMULA
Equals row sums of triangle A155810.
a(n) = (1/n)*Sum_{k=1..n} (2^k + 1)^k * a(n-k) for n>0, with a(0)=1.
a(n) = B_n( 0!*(2^1+1)^1, 1!*(2^2+1)^2, 2!*(2^3+1)^3, ..., (n-1)!*(2^n+1)^n ) / n!, where B_n() is the n-th complete Bell polynomial. - Max Alekseyev, Oct 10 2014
EXAMPLE
G.f.: A(x) = 1 + 3*x + 17*x^2 + 285*x^3 + 21747*x^4 + 7894143*x^5 +...
log(A(x)) = 3*x + 5^2*x^2/2 + 9^3*x^3/3 + 17^4*x^4/4 + 33^5*x^5/5 +...
PROG
(PARI) {a(n)=polcoeff(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 04 2009
STATUS
approved