A208056 G.f.: exp( Sum_{n>=1} 2*Pell(n)^(2*n) * x^n/n ), where Pell(n) = A000129(n).

1, 2, 18, 10450, 215011842, 168283323489554, 4613762736903044410402, 4429409381416783893511092430530, 147401742703370819998531165821635082467298, 169293247178836261713452084817353169649400098579929282

Offset: 0

Author

Paul D. Hanna, Feb 22 2012

Keywords

• nonn

Comments

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

Examples

			G.f.: A(x) = 1 + 2*x + 18*x^2 + 10450*x^3 + 215011842*x^4 +...
such that, by definition,
log(A(x))/2 = x + 2^4*x^2/2 + 5^6*x^3/3 + 12^8*x^4/4 + 29^10*x^5/5 + 70^12*x^6/6 + 169^14*x^7/7 +...+ Pell(n)^(2*n)*x^n/n +...
		

Crossrefs

Cf. A000129, A211891, A208034, A208055, A204061, A204062.

Programs

PARI

{Pell(n)=polcoeff(x/(1-2*x-x^2 +x*O(x^n)),n)}
{a(n)=polcoeff(exp(sum(m=1,n,2*Pell(m)^(2*m)*x^m/m) +x*O(x^n)),n)}
for(n=0,15,print1(a(n),", "))