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A155204 G.f.: A(x) = exp( Sum_{n>=1} (3^n + 1)^n * x^n/n ), a power series in x with integer coefficients. 7

%I #2 Mar 30 2012 18:37:15

%S 1,4,58,7528,11333974,173018964568,25223063625377572,

%T 34295288559321731710864,429734241619476967064512081894,

%U 49292144502053186639397817183561560472

%N G.f.: A(x) = exp( Sum_{n>=1} (3^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.

%F Equals row sums of triangle A155812.

%e G.f.: A(x) = 1 + 4*x + 58*x^2 + 7528*x^3 + 11333974*x^4 + 173018964568*x^5 +...

%e log(A(x)) = 4*x + 10^2*x^2/2 + 28*x^3/3 + 82^4*x^4/4 + 244^5*x^5/5 +...

%o (PARI) {a(n)=polcoeff(exp(sum(m=1,n+1,(3^m+1)^m*x^m/m)+x*O(x^n)),n)}

%Y Cf. A155203, A155205, A155206, A155812 (triangle), variants: A155201, A155208.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Feb 04 2009

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)