A096971 G.f. satisfies: A(x) = A( x^2*A000108(x^2) )*x*A000984(x^2), where A000108(x) is the g.f. for the Catalan sequence and A000984(x) = d/dx x*A000108(x).

1, 1, 4, 13, 49, 181, 685, 2605, 9988, 38479, 148879, 577930, 2249698, 8777614, 34315012, 134377393, 526994773, 2069403898, 8135377102, 32014655626, 126099239329, 497083313908, 1960943833567, 7740893831005, 30576064032568

Offset

0,3

Links

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

R. Resch, F. Stenger and J. Waldvogel, 1996, page 8, Functional Equations Related to the Iteration of Functions.

Formula

a(n) = Sum_{j=0..[(n+1)/2]} C(2*n-2*j-1, n-1)*a(j), a(0)=a(1)=1. G.f. satisfies: A(x) = A( (1-sqrt(1-4*x^2))/2 )*x/sqrt(1-4*x^2), where A(x) = Sum_{n>=0} a(n)*x^(2*n-1).

Example

A(x) = x^-1 + x + 4*x^3 + 13*x^5 + 49*x^7 + 181*x^9 + 685*x^11 +...

Prog

(PARI) a(n)=if(n==0 || n==1, 1, sum(j=0, (n+1)\2, binomial(2*n-2*j-1, n-1)*a(j)))

Crossrefs

Sequence in context: A180007 A338862 A097948 * A149451 A149452 A140660

Adjacent sequences: A096968 A096969 A096970 * A096972 A096973 A096974

Keyword

nonn

Author

Paul D. Hanna, Jul 16 2004

Status

approved