A143564 G.f. satisfies: A(x) = 1 + x*A(x)^4/A(-x)^3.

1, 1, 7, 31, 273, 1697, 16471, 116159, 1186081, 8928193, 94017703, 736522975, 7917810225, 63722594657, 695248655095, 5705316231551, 62944217175617, 524183926274433, 5833380674885959, 49141433498848159, 550674827214221137

Offset: 0

Author

Paul D. Hanna, Aug 24 2008

Keywords

• nonn

Examples

			G.f. A(x) = 1 + x + 7*x^2 + 31*x^3 + 273*x^4 + 1697*x^5 +...
A(x)*A(-x) = 1 + 13*x^2 + 533*x^4 + 32409*x^6 + 2339753*x^8 +...
		

Crossrefs

Cf. A143557, A143562.

Programs

PARI

{a(n)=local(A=1+x*O(x^n));for(i=0,n,A=1+x*A^4/subst(A^3,x,-x));polcoeff(A,n)}

Formula

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

G.f.: A(x) = G(x)/(1+x^2) where G(x) = 1 + x*G(x)^4/G(-x)^4 is the g.f. of A143557.