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.

1, 2, 6, 20, 166, 1980, 91612, 4980968, 1083899526, 246514209900, 225675208005684, 210073940172966552, 787481680820307364188, 2977392786568558334126040, 45279192083837920124027862264

Offset: 0

Author

Paul D. Hanna, Feb 10 2009

Keywords

• nonn

Examples

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

Crossrefs

Cf. A156340, A155200.

Programs

PARI

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

Formula

a(n) = (1/n)*Sum_{k=1..n} 2^floor(k^2/2+1) * a(n-k) for n>0, with a(0)=1.