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A208055 G.f.: exp( Sum_{n>=1} 2*Pell(n)^4 * x^n/n ), where Pell(n) = A000129(n).

%I A208055 #13 Oct 31 2024 10:43:38
%S A208055 1,2,18,450,11362,311426,8857426,259072706,7730804098,234255654466,
%T A208055 7184570715602,222512186923010,6947171244623714,218374183252085826,
%U A208055 6903938704875627410,219355658720815861378,6999679608428089841154,224210965624588803552642
%N A208055 G.f.: exp( Sum_{n>=1} 2*Pell(n)^4 * x^n/n ), where Pell(n) = A000129(n).
%F A208055 The o.g.f. A(x) = 1 + 2*x + 18*x^2 + 450*x^3 + ... is an algebraic function: A(x)^32 = (1 + 6*x + x^2)^4/( (1 - 34*x + x^2)*(1 - 2*x + x^2)^3 ). Cf. A207969. - _Peter Bala_, Apr 03 2014
%F A208055 From _Vaclav Kotesovec_, Oct 31 2024: (Start)
%F A208055 G.f.: (1 + x*(6 + x))^(1/8) / ((1 - x)^(3/16)*(1 + (-17 + 12*sqrt(2))*x)^(1/32) * (1 - (17 + 12*sqrt(2))*x)^(1/32)).
%F A208055 a(n) ~ 5^(1/8) * (1 + sqrt(2))^(4*n) / (2^(13/64) * 3^(1/32) * Gamma(1/32) * n^(31/32)). (End)
%e A208055 G.f.: A(x) = 1 + 2*x + 18*x^2 + 450*x^3 + 11362*x^4 + 311426*x^5 +...
%e A208055 such that, by definition,
%e A208055 log(A(x))/2 = x + 2^4*x^2/2 + 5^4*x^3/3 + 12^4*x^4/4 + 29^4*x^5/5 + 70^4*x^6/6 + 169^4*x^7/7 + 408^4*x^8/8 +...+ Pell(n)^4*x^n/n +...
%o A208055 (PARI) {Pell(n)=polcoeff(x/(1-2*x-x^2 +x*O(x^n)),n)}
%o A208055 {a(n)=polcoeff(exp(sum(m=1,n,2*Pell(m)^4*x^m/m) +x*O(x^n)),n)}
%o A208055 for(n=0,30,print1(a(n),", "))
%Y A208055 Cf. A000129, A208034, A208056, A204061, A204062, A207969.
%K A208055 nonn
%O A208055 0,2
%A A208055 _Paul D. Hanna_, Feb 22 2012