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

0,4

Comments

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

Links

Table of n, a(n) for n=0..27.

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

Crossrefs

Cf. A101499, A102879.

Sequence in context: A301555 A261561 A017928 * A137104 A265951 A178159

Adjacent sequences: A102877 A102878 A102879 * A102881 A102882 A102883

Keyword

easy,nonn

Author

Paul Barry, Jan 15 2005

Status

approved