cp's OEIS Frontend

A155206 G.f.: A(x) = exp( Sum_{n>=1} (3^n - 1)^n/2^(n-1) * x^n/n ), a power series in x with integer coefficients.

%I A155206 #2 Mar 30 2012 18:37:15
%S A155206 1,2,18,1498,1283090,10377556482,775351592888722,
%T A155206 532444511048570910746,3349121447720205394546014978,
%U A155206 192371436319107536207473420480152034,100642626897912335112447860229547933463000450
%N A155206 G.f.: A(x) = exp( Sum_{n>=1} (3^n - 1)^n/2^(n-1) * x^n/n ), a power series in x with integer coefficients.
%C A155206 More generally, for m integer, exp( Sum_{n>=1} (m^n - 1)^n/(m-1)^(n-1) * x^n/n ) is a power series in x with integer coefficients.
%C A155206 Note that g.f. exp( Sum_{n>=1} (3^n - 1)^n/2^n * x^n/n ) has fractional coefficients as a power series in x.
%e A155206 G.f.: A(x) = 1 + 2*x + 18*x^2 + 1498*x^3 + 1283090*x^4 + 10377556482*x^5 +...
%e A155206 log(A(x)) = 2*x + 8^2/2*x^2/2 + 26^3/2^2*x^3/3 + 80^4/2^3*x^4/4 + 242^5/2^4*x^5/5 +...
%o A155206 (PARI) {a(n)=polcoeff(exp(sum(m=1,n+1,(3^m-1)^m/2^(m-1)*x^m/m)+x*O(x^n)),n)}
%Y A155206 Cf. A155203, A155204, A155205, A155812 (triangle), variant: A155210.
%K A155206 nonn
%O A155206 0,2
%A A155206 _Paul D. Hanna_, Feb 04 2009