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A366733 Expansion of g.f. A(x) satisfying 0 = Sum_{n=-oo..+oo} x^n * A(x)^n * (3 - x^(n-1))^(n+1).

%I A366733 #5 Oct 29 2023 22:02:33
%S A366733 1,3,12,90,702,5838,50895,458103,4225683,39745665,379730658,
%T A366733 3674980518,35951809104,354950991006,3532167377340,35390917028619,
%U A366733 356742401734236,3615164398809324,36809446799831823,376387507560832992,3863438843523528636,39794189982905311407
%N A366733 Expansion of g.f. A(x) satisfying 0 = Sum_{n=-oo..+oo} x^n * A(x)^n * (3 - x^(n-1))^(n+1).
%C A366733 a(n) = Sum_{k=0..n} A366730(n,k) * 3^k for n >= 0.
%F A366733 G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies the following formulas.
%F A366733 (1) 0 = Sum_{n=-oo..+oo} x^n * A(x)^n * (3 - x^(n-1))^(n+1).
%F A366733 (2) 0 = Sum_{n=-oo..+oo} (-1)^n * x^(n*(n-1)) / ( A(x)^n * (1 - 3*x^(n+1))^(n-1) ).
%e A366733 G.f.: A(x) = 1 + 3*x + 12*x^2 + 90*x^3 + 702*x^4 + 5838*x^5 + 50895*x^6 + 458103*x^7 + 4225683*x^8 + 39745665*x^9 + 379730658*x^10 + ...
%o A366733 (PARI) {a(n) = my(A=[1]); for(i=1,n, A = concat(A,0);
%o A366733 A[#A] = polcoeff( sum(n=-#A,#A, x^n * Ser(A)^n * (3 - x^(n-1))^(n+1) ), #A-2));A[n+1]}
%o A366733 for(n=0,30,print1(a(n),", "))
%Y A366733 Cf. A366730, A366731, A366732, A366734, A366735.
%K A366733 nonn
%O A366733 0,2
%A A366733 _Paul D. Hanna_, Oct 29 2023