cp's OEIS Frontend

A155208 G.f.: A(x) = exp( Sum_{n>=1} (4^n + 1)^n * x^n/n ), a power series in x with integer coefficients.

%I A155208 #2 Mar 30 2012 18:37:15
%S A155208 1,5,157,92285,1091087581,226287110093405,788215837483128170845,
%T A155208 45292586018794926904179045725,42540488665745908362239138191829777245,
%U A155208 649578584556365450465861374646071307864262693725
%N A155208 G.f.: A(x) = exp( Sum_{n>=1} (4^n + 1)^n * x^n/n ), a power series in x with integer coefficients.
%C A155208 More generally, 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.
%e A155208 G.f.: A(x) = 1 + 5*x + 157*x^2 + 92285*x^3 + 1091087581*x^4 +...
%e A155208 log(A(x)) = 5*x + 17^2*x^2/2 + 65^3*x^3/3 + 257^4*x^4/4 + 1025^5*x^5/5 +...
%o A155208 (PARI) {a(n)=polcoeff(exp(sum(m=1,n+1,(4^m+1)^m*x^m/m)+x*O(x^n)),n)}
%Y A155208 Cf. A155207, A155209, A155210, variants: A155201, A155204.
%K A155208 nonn
%O A155208 0,2
%A A155208 _Paul D. Hanna_, Feb 04 2009