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%I #9 Nov 23 2018 11:29:14
%S 1,1,1,3,11,50,294,1833,13093,100456,830541,7313419,68137388,
%T 668327844,6873073257,73853969234,826869429175,9622413867975,
%U 116144019094407,1451337070767512,18744666092043742,249848115448337748,3432213607060089249,48532637291552045262,705602120522021975822,10536473807470843781980,161442021516682347676435
%N G.f.: A(x) = Sum_{n>=0} x^n * (1+x)^(2*n^2) / A(x)^(2*n).
%H Paul D. Hanna, <a href="/A321607/b321607.txt">Table of n, a(n) for n = 0..200</a>
%e G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 11*x^4 + 50*x^5 + 294*x^6 + 1833*x^7 + 13093*x^8 + 100456*x^9 + 830541*x^10 + 7313419*x^11 + 68137388*x^12 + ...
%e such that
%e A(x) = 1 + x*(1+x)^2/A(x)^2 + x^2*(1+x)^8/A(x)^4 + x^3*(1+x)^18/A(x)^6 + x^4*(1+x)^32/A(x)^8 + x^5*(1+x)^50/A(x)^10 + x^6*(1+x)^72/A(x)^12 + ...
%o (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)^(2*n+1) ) )[#A] ); A[n+1]}
%o for(n=0, 30, print1(a(n), ", "))
%Y Cf. A303058, A321608.
%K nonn
%O 0,4
%A _Paul D. Hanna_, Nov 23 2018
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