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

1, 1, 3, 22, 115, 1048, 6418, 63784, 421195, 4386273, 30271136, 324599018, 2306033386, 25228297188, 182938978344, 2030788315648, 14952369357211, 167836915812087, 1250429798513035, 14158770843121424, 106483223789898776

Offset: 0

Author

Paul D. Hanna, Aug 24 2008

Keywords

• nonn

Examples

			G.f. A(x) = 1 + x + 3*x^2 + 22*x^3 + 115*x^4 + 1048*x^5 + 6418*x^6 +...
Related expansions:
A(x)^5 = 1 + 5*x + 25*x^2 + 180*x^3 + 1200*x^4 + 9851*x^5 + 73195*x^6 +...
A(-x)^2 = 1 - 2*x + 7*x^2 - 50*x^3 + 283*x^4 - 2458*x^5 + 16106*x^6 -+...
A(x)*A(-x) = 1 + 5*x^2 + 195*x^4 + 10946*x^6 + 720443*x^8 +...
[A(x)*A(-x)]^7 = 1 + 35*x^2 + 1890*x^4 + 121947*x^6 + 8674036*x^8 +...
		

Crossrefs

Cf. A143550, A143551, A143553, A143554.

Programs

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)}

Formula

G.f. satisfies: A(x) + A(-x) = 1 + [A(x)*A(-x)] + x^2*[A(x)*A(-x)]^7.

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