A143561 G.f. satisfies: A(x) = ( 1 + x*A(x)/A(-x) )^2.

1, 2, 9, 24, 88, 280, 1064, 3672, 14456, 52184, 210504, 782232, 3210904, 12176792, 50638440, 194956248, 818961080, 3189915224, 13508052104, 53105011480, 226355549400, 896636646936, 3842662060200, 15317408281944, 65946510374136

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

G.f. satisfies: (1+x^2)^2 - 2*(1+x^2)*G(x) + (1+x)*G(x)^2 - x*G(x)^3 = 0 where G(x)^2 = A(x) and G(x) = 1 + x*A(x)/A(-x) is the g.f. of A143555.

Example

G.f.: A(x) = 1 + 2*x + 9*x^2 + 24*x^3 + 88*x^4 + 280*x^5 + 1064*x^6 +...
A(x)/A(-x) = 1 + 4*x + 8*x^2 + 28*x^3 + 80*x^4 + 308*x^5 + 984*x^6 +...

Prog

(PARI) {a(n)=local(A=1+x*O(x^n)); for(i=0, n, B=A/subst(A, x, -x); A=(1+x*B)^2); polcoeff(A, n)}

Crossrefs

Cf. A143555.

Sequence in context: A222667 A122006 A200086 * A363660 A027302 A374703

Adjacent sequences: A143558 A143559 A143560 * A143562 A143563 A143564

Keyword

nonn

Author

Paul D. Hanna, Aug 24 2008

Status

approved