A102880 A Chebyshev transform of the first kind of the Catalan numbers.

1, 1, 0, 2, 8, 22, 64, 198, 624, 1994, 6464, 21210, 70296, 234990, 791424, 2682894, 9147360, 31347730, 107919232, 373055730, 1294372008, 4506163718, 15735793088, 55105084246, 193471595344, 680891484762, 2401575077568, 8487950090954

Offset: 0

Author

Paul Barry, Jan 15 2005

Keywords

• easy
• nonn

Comments

Image of c(x) under the mapping g(x)->((1-x^2)/(1+x^2))g(x/(1+x^2)).

Crossrefs

Cf. A101499, A102879.

Formula

G.f.: ((1-x^2)/(1+x^2))c(x/(1+x^2)), c(x) the g.f. of the Catalan numbers A000108; a(n)=n*sum{k=0..floor(n/2), C(n-k, k)(-1)^k*C(n-2k)/(n-k)}.

Conjecture: (n+1)*(n-3)*a(n) -2*(2*n-1)*(n-3)*a(n-1) +2*(1-4*n+n^2)*a(n-2) -2*(n-1)*(2*n-7)*a(n-3) +(n-1)*(n-5)*a(n-4)=0. - R. J. Mathar, Nov 09 2012