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A155208 G.f.: A(x) = exp( Sum_{n>=1} (4^n + 1)^n * x^n/n ), a power series in x with integer coefficients. 5

%I

%S 1,5,157,92285,1091087581,226287110093405,788215837483128170845,

%T 45292586018794926904179045725,42540488665745908362239138191829777245,

%U 649578584556365450465861374646071307864262693725

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

%C 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 G.f.: A(x) = 1 + 5*x + 157*x^2 + 92285*x^3 + 1091087581*x^4 +...

%e 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 (PARI) {a(n)=polcoeff(exp(sum(m=1,n+1,(4^m+1)^m*x^m/m)+x*O(x^n)),n)}

%Y Cf. A155207, A155209, A155210, variants: A155201, A155204.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Feb 04 2009

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Last modified January 18 19:40 EST 2020. Contains 331029 sequences. (Running on oeis4.)