A102880 - OEIS

%I #6 Nov 09 2012 12:12:08

%S 1,1,0,2,8,22,64,198,624,1994,6464,21210,70296,234990,791424,2682894,

%T 9147360,31347730,107919232,373055730,1294372008,4506163718,

%U 15735793088,55105084246,193471595344,680891484762,2401575077568,8487950090954

%N A Chebyshev transform of the first kind of the Catalan numbers.

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

%F 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)}.

%F 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

%Y Cf. A101499, A102879.

%K easy,nonn

%O 0,4

%A _Paul Barry_, Jan 15 2005