A143551 G.f. A(x) satisfies A(x) = 1 + x*A(x)^5*A(-x).

1, 1, 4, 29, 196, 1781, 14000, 139234, 1176340, 12283166, 108258380, 1165438808, 10561185568, 116096795195, 1072964739264, 11975785105572, 112313638368948, 1268177365551626, 12029082865935512, 137067430786661911

Offset: 0

Author

Paul D. Hanna, Aug 24 2008

Keywords

• nonn

Examples

			G.f. A(x) = 1 + x + 4*x^2 + 29*x^3 + 196*x^4 + 1781*x^5 + 14000*x^6 +...
Related expansions:
A(x)^5 = 1 + 5*x + 30*x^2 + 235*x^3 + 1845*x^4 + 16576*x^5 + 144270*x^6 +...
A(x)*A(-x) = 1 + 7*x^2 + 350*x^4 + 25165*x^6 + 2121330*x^8 +...
[A(x)*A(-x)]^6 = 1 + 42*x^2 + 2835*x^4 + 231350*x^6 +...
		

Crossrefs

Cf. A143550, A143552, A143553, A143554.

Programs

PARI

{a(n)=local(A=1+x*O(x^n));for(i=0,n,A=1+x*A^5*subst(A,x,-x));polcoeff(A,n)}

Formula

G.f. satisfies: A(x) + A(-x) = 1 + [A(x)*A(-x)] + x^2*[A(x)*A(-x)]^6.

a(0) = 1; a(n) = Sum_{x_1, x_2, ..., x_6>=0 and x_1+x_2+...+x_6=n-1} (-1)^x_1 * Product_{k=1..6} a(x_k). - Seiichi Manyama, Jul 08 2025