A143558 G.f. satisfies: A(x) = 1 + x*A(x)^5/A(-x)^5.

1, 1, 10, 50, 570, 4450, 56202, 501970, 6676410, 63799490, 875391370, 8715058802, 122088479930, 1249437863970, 17764858122250, 185445650940690, 2666213981716282, 28252030821781890, 409717783914784010

Offset: 0

Author

Paul D. Hanna, Aug 24 2008

Keywords

• nonn

Examples

			G.f. A(x) = 1 + x + 10*x^2 + 50*x^3 + 570*x^4 + 4450*x^5 + 56202*x^6 +...
A(x)/A(-x) = 1 + 2*x + 2*x^2 + 82*x^3 + 162*x^4 + 7202*x^5 + 17442*x^6 +...
A(x)^4/A(-x)^4 = 1 + 8*x + 32*x^2 + 408*x^3 + 2752*x^4 + 38760*x^5 +...
where 1 - (1+x^2)/A(x) = x*A(x)^4/A(-x)^4.
		

Crossrefs

Cf. A143555, A143556, A143557, A143559.

Programs

PARI

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

Formula

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

G.f. satisfies: A(x) = 1 + x^2 + x*A(x)^5/A(-x)^4.

G.f. satisfies: (A(x) - 1)^4 = ( 1 - (1+x^2)/A(x) )^5/x = x^4*A(x)^20/A(-x)^20.

G.f.: A(x) = (1+x^2)*G(x) where G(x) = 1 + x*G(x)^5/G(-x)^4.