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A102880
A Chebyshev transform of the first kind of the Catalan numbers.
1
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)).
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
Sequence in context: A301555 A261561 A017928 * A137104 A265951 A178159
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jan 15 2005
STATUS
approved