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

%I

%S 1,2,14,682,236826,525175434,7101054148862,575978478770467714,

%T 277997363115795461721154,794462328877965002894838885122,

%U 13398419999037765629218732004567606814,1330302023374557034879527995005574743144202826

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

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

%e G.f.: A(x) = 1 + 2*x + 14*x^2 + 682*x^3 + 236826*x^4 + 525175434*x^5 +...

%e such that

%e 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 +...

%e Pell numbers begin:

%e A000129 = [1,2,5,12,29,70,169,408,985,2378,5741,13860,33461,...].

%o (PARI) {Pell(n)=polcoeff(x/(1-2*x-x^2+x*O(x^n)),n)}

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

%o for(n=0, 20, print1(a(n), ", "))

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

%K nonn

%O 0,2

%A _Paul D. Hanna_, Apr 24 2012

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Last modified September 19 10:53 EDT 2021. Contains 347556 sequences. (Running on oeis4.)