cp's OEIS Frontend

A156334 G.f.: A(x) = exp( Sum_{n>=1} 2^[n^2/2+1]*x^n/n ), a power series in x with integer coefficients.

%I A156334 #5 Jan 16 2013 07:51:12
%S A156334 1,2,6,20,166,1980,91612,4980968,1083899526,246514209900,
%T A156334 225675208005684,210073940172966552,787481680820307364188,
%U A156334 2977392786568558334126040,45279192083837920124027862264
%N A156334 G.f.: A(x) = exp( Sum_{n>=1} 2^[n^2/2+1]*x^n/n ), a power series in x with integer coefficients.
%F A156334 a(n) = (1/n)*Sum_{k=1..n} 2^floor(k^2/2+1) * a(n-k) for n>0, with a(0)=1.
%e A156334 G.f.: A(x) = 1 + 2*x + 6*x^2 + 20*x^3 + 166*x^4 + 1980*x^5 + 91612*x^6 +...
%e A156334 log(A(x)) = 2*x + 2^3*x^2/2 + 2^5*x^3/3 + 2^9*x^4/4 + 2^13*x^5/5 + 2^19*x^6/6 +...
%o A156334 (PARI) {a(n)=polcoeff(exp(sum(k=1, n, 2^floor(k^2/2+1)*x^k/k)+x*O(x^n)), n)}
%Y A156334 Cf. A156340, A155200.
%K A156334 nonn
%O A156334 0,2
%A A156334 _Paul D. Hanna_, Feb 10 2009