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Numerators in expansion of (1+x-sqrt(1-x^2))/(x(1-x)).
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%I #2 Mar 30 2012 18:59:21

%S 1,3,3,13,13,27,27,221,221,449,449,1817,1817,3667,3667,59101,59101,

%T 118917,118917,478099,478099,960397,960397,7712569,7712569,15477141,

%U 15477141,62094289,62094289,124522883,124522883,3994427101

%N Numerators in expansion of (1+x-sqrt(1-x^2))/(x(1-x)).

%C The denominators in the expansion of (1+x-sqrt(1-x^2))/(x(1-x)) are 1,2,2,8,8,16,16,....

%C The sequence 1,3/2,3/2,13/8,13/8,... is the image of 2n+1 under the

%C Chebyshev related (rational) Riordan array c((x/2)^2),(x/2)c((x/2)^2)) with c(x) the g.f. of A000108.

%C The Hankel transform of fraction sequence is (-1)^n*(2n+1)/4^comb(n+1,2).

%Y Cf. A141244.

%K easy,frac,nonn

%O 0,2

%A _Paul Barry_, Jun 17 2008