A211891 G.f.: exp( Sum_{n>=1} 2 * Pell(n^2) * x^n/n ), where Pell(n) = A000129(n).

1, 2, 14, 682, 236826, 525175434, 7101054148862, 575978478770467714, 277997363115795461721154, 794462328877965002894838885122, 13398419999037765629218732004567606814, 1330302023374557034879527995005574743144202826

Offset: 0

Author

Paul D. Hanna, Apr 24 2012

Keywords

• nonn

Comments

Given g.f. A(x), note that A(x)^(1/2) is not an integer series.

Examples

			G.f.: A(x) = 1 + 2*x + 14*x^2 + 682*x^3 + 236826*x^4 + 525175434*x^5 +...
such that
log(A(x))/2 = x + 12*x^2/2 + 985*x^3/3 + 470832*x^4/4 + 1311738121*x^5/5 + 21300003689580*x^6/6 + 2015874949414289041*x^7/7 +...+ Pell(n^2)*x^n/n +...
Pell numbers begin:
A000129 = [1,2,5,12,29,70,169,408,985,2378,5741,13860,33461,...].
		

Crossrefs

Cf. A208056, A211892, A000129 (Pell), A204327 (Pell(n^2)).

Programs

PARI

{Pell(n)=polcoeff(x/(1-2*x-x^2+x*O(x^n)),n)}
{a(n)=polcoeff(exp(sum(k=1, n, 2*Pell(k^2)*x^k/k)+x*O(x^n)), n)}
for(n=0, 20, print1(a(n), ", "))