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A366734 Expansion of g.f. A(x) satisfying 0 = Sum_{n=-oo..+oo} x^n * A(x)^n * (4 - x^(n-1))^(n+1).

%I A366734 #5 Oct 29 2023 22:02:41
%S A366734 1,4,24,236,2504,28332,335656,4108688,51558000,659737684,8575826448,
%T A366734 112927383328,1503232394344,20195196226124,273467339844368,
%U A366734 3728623506924660,51145851271818536,705322823588365592,9772995790887474920,135992755093954566300,1899633478390401668072
%N A366734 Expansion of g.f. A(x) satisfying 0 = Sum_{n=-oo..+oo} x^n * A(x)^n * (4 - x^(n-1))^(n+1).
%C A366734 a(n) = Sum_{k=0..n} A366730(n,k) * 4^k for n >= 0.
%F A366734 G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies the following formulas.
%F A366734 (1) 0 = Sum_{n=-oo..+oo} x^n * A(x)^n * (4 - x^(n-1))^(n+1).
%F A366734 (2) 0 = Sum_{n=-oo..+oo} (-1)^n * x^(n*(n-1)) / ( A(x)^n * (1 - 4*x^(n+1))^(n-1) ).
%e A366734 G.f.: A(x) = 1 + 4*x + 24*x^2 + 236*x^3 + 2504*x^4 + 28332*x^5 + 335656*x^6 + 4108688*x^7 + 51558000*x^8 + 659737684*x^9 + 8575826448*x^10 + ...
%o A366734 (PARI) {a(n) = my(A=[1]); for(i=1,n, A = concat(A,0);
%o A366734 A[#A] = polcoeff( sum(n=-#A,#A, x^n * Ser(A)^n * (4 - x^(n-1))^(n+1) ), #A-2));A[n+1]}
%o A366734 for(n=0,30,print1(a(n),", "))
%Y A366734 Cf. A366730, A366731, A366732, A366733, A366735.
%K A366734 nonn
%O A366734 0,2
%A A366734 _Paul D. Hanna_, Oct 29 2023