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A321608 G.f.: A(x) = Sum_{n>=0} x^n * (1+x)^(2*n^2) / A(x)^n.

%I A321608 #4 Nov 23 2018 09:05:46
%S A321608 1,1,2,5,22,100,581,3716,26352,203664,1688485,14922599,139579911,
%T A321608 1374581231,14194823072,153178320198,1722363891798,20130227813033,
%U A321608 244028318224686,3062549991414408,39723783490631858,531726501000859625,7335052105035725087,104148717578191099492,1520349684313678309811,22793632534841442908565,350622445923759834928352,5528760266814203384425285
%N A321608 G.f.: A(x) = Sum_{n>=0} x^n * (1+x)^(2*n^2) / A(x)^n.
%H A321608 Paul D. Hanna, <a href="/A321608/b321608.txt">Table of n, a(n) for n = 0..200</a>
%e A321608 G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 22*x^4 + 100*x^5 + 581*x^6 + 3716*x^7 + 26352*x^8 + 203664*x^9 + 1688485*x^10 + 14922599*x^11 + 139579911*x^12 + ...
%e A321608 such that
%e A321608 A(x) = 1 + x*(1+x)^2/A(x) + x^2*(1+x)^8/A(x)^2 + x^3*(1+x)^18/A(x)^3 + x^4*(1+x)^32/A(x)^4 + x^5*(1+x)^50/A(x)^5 + x^6*(1+x)^72/A(x)^6 + ...
%o A321608 (PARI) {a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0); A[#A] = Vec(sum(n=0, #A, ((1+x)^n +x*O(x^#A))^(2*n) * x^n/Ser(A)^(n+1) ) )[#A] ); A[n+1]}
%o A321608 for(n=0, 30, print1(a(n), ", "))
%Y A321608 Cf. A303058, A321607.
%K A321608 nonn
%O A321608 0,3
%A A321608 _Paul D. Hanna_, Nov 23 2018