%I #5 Jan 16 2013 07:51:12

%S 1,2,6,20,166,1980,91612,4980968,1083899526,246514209900,

%T 225675208005684,210073940172966552,787481680820307364188,

%U 2977392786568558334126040,45279192083837920124027862264

%N 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 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 G.f.: A(x) = 1 + 2*x + 6*x^2 + 20*x^3 + 166*x^4 + 1980*x^5 + 91612*x^6 +...

%e 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 (PARI) {a(n)=polcoeff(exp(sum(k=1, n, 2^floor(k^2/2+1)*x^k/k)+x*O(x^n)), n)}

%Y Cf. A156340, A155200.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Feb 10 2009