A155205 - OEIS

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

%S 1,2,34,5924,10252294,166020197708,24810918565918804,

%T 34076399079565985138408,428687477154543524080261047622,

%U 49247086840315416213775472777558582540

%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.

%e G.f.: A(x) = 1 + 2*x + 34*x^2 + 5924*x^3 + 10252294*x^4 +...

%e log(A(x)) = 2*x + 8^2*x^2/2 + 26^3*x^3/3 + 80^4*x^4/4 + 242^5*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, A155204, A155206, A155812 (triangle), variants: A155202, A155209.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Feb 04 2009