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%I #5 Dec 08 2022 07:34:35
%S 1,3,21,159,1369,12131,111489,1042310,9878188,94345595,905236045,
%T 8698907855,83509981377,798911473287,7596665295846,71585365842419,
%U 666055801137389,6089025714101416,54304588402962717,467144137463862047,3798557443794080777,27983895459969702990
%N a(n) = coefficient of x^n in A(x) such that: 0 = Sum_{n=-oo..+oo} x^(3*n) * (x^n - 2*A(x))^(4*n+1).
%C Related identity: 0 = Sum_{n=-oo..+oo} x^n * (y - x^n)^n, which holds formally for all y.
%F G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies:
%F (1) 0 = Sum_{n=-oo..+oo} x^(3*n) * (x^n - 2*A(x))^(4*n+1).
%F (2) 0 = Sum_{n=-oo..+oo} x^(4*n*(n-1)) / (1 - 2*A(x)*x^n)^(4*n-1).
%e G.f.: A(x) = 1 + 3*x + 21*x^2 + 159*x^3 + 1369*x^4 + 12131*x^5 + 111489*x^6 + 1042310*x^7 + 9878188*x^8 + 94345595*x^9 + 905236045*x^10 + ...
%o (PARI) {a(n) = my(A=[1]); for(i=1,n, A=concat(A,0);
%o A[#A] = polcoeff( sum(n=-#A,#A, x^(3*n) * (x^n - 2*Ser(A))^(4*n+1) ), #A-1)/2);A[n+1]}
%o for(n=0,25,print1(a(n),", "))
%Y Cf. A355865, A358952, A358954, A358955, A358956, A358957, A358958, A358959.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Dec 07 2022
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