A132332 G.f.: A(x) = A_1 where A_1 = 1/[1 - x*(A_2)^2], A_2 = 1/[1 - x^2*(A_3)^2], A_3 = 1/[1 - x^3*(A_4)^2], ... A_n = 1/[1 - x^n*(A_{n+1})^2] for n>=1.

1, 1, 1, 3, 5, 10, 23, 44, 93, 193, 398, 828, 1711, 3548, 7352, 15238, 31569, 65414, 135557, 280856, 581970, 1205860, 2498520, 5177008, 10726715, 22225674, 46051484, 95417966, 197704676, 409640915, 848768686, 1758633069, 3643854113

Offset: 0

Author

Paul D. Hanna, Aug 20 2007

Keywords

• nonn

Crossrefs

Cf. A132333 (self-convolution); A132334 (variant).

Programs

PARI

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

PARI

N = 66;  q = 'q + O('q^N);
G(k) = if(k>N, 1, 1 - q^(k+1) / G(k+1)^2 );
gf = 1 / G(0);
Vec(gf) \\ Joerg Arndt, Jul 06 2013

Formula

G.f.: 1/G(0) where G(k) = 1 - q^(k+1) / G(k+1)^2. [Joerg Arndt, Jul 06 2013]