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A143552 G.f. A(x) satisfies A(x) = 1 + x*A(x)^5*A(-x)^2.

%I A143552 #6 Jul 08 2025 07:41:34
%S A143552 1,1,3,22,115,1048,6418,63784,421195,4386273,30271136,324599018,
%T A143552 2306033386,25228297188,182938978344,2030788315648,14952369357211,
%U A143552 167836915812087,1250429798513035,14158770843121424,106483223789898776
%N A143552 G.f. A(x) satisfies A(x) = 1 + x*A(x)^5*A(-x)^2.
%F A143552 G.f. satisfies: A(x) + A(-x) = 1 + [A(x)*A(-x)] + x^2*[A(x)*A(-x)]^7.
%F A143552 a(0) = 1; a(n) = Sum_{x_1, x_2, ..., x_7>=0 and x_1+x_2+...+x_7=n-1} (-1)^(x_1+x_2) * Product_{k=1..7} a(x_k). - _Seiichi Manyama_, Jul 08 2025
%e A143552 G.f. A(x) = 1 + x + 3*x^2 + 22*x^3 + 115*x^4 + 1048*x^5 + 6418*x^6 +...
%e A143552 Related expansions:
%e A143552 A(x)^5 = 1 + 5*x + 25*x^2 + 180*x^3 + 1200*x^4 + 9851*x^5 + 73195*x^6 +...
%e A143552 A(-x)^2 = 1 - 2*x + 7*x^2 - 50*x^3 + 283*x^4 - 2458*x^5 + 16106*x^6 -+...
%e A143552 A(x)*A(-x) = 1 + 5*x^2 + 195*x^4 + 10946*x^6 + 720443*x^8 +...
%e A143552 [A(x)*A(-x)]^7 = 1 + 35*x^2 + 1890*x^4 + 121947*x^6 + 8674036*x^8 +...
%o A143552 (PARI) {a(n)=local(A=1+x*O(x^n));for(i=0,n,A=1+x*A^5*subst(A^2,x,-x));polcoeff(A,n)}
%Y A143552 Cf. A143550, A143551, A143553, A143554.
%K A143552 nonn
%O A143552 0,3
%A A143552 _Paul D. Hanna_, Aug 24 2008