A141245 Numerators in expansion of (1+x-sqrt(1-x^2))/(x(1-x)).

1, 3, 3, 13, 13, 27, 27, 221, 221, 449, 449, 1817, 1817, 3667, 3667, 59101, 59101, 118917, 118917, 478099, 478099, 960397, 960397, 7712569, 7712569, 15477141, 15477141, 62094289, 62094289, 124522883, 124522883, 3994427101

Offset: 0

Author

Paul Barry, Jun 17 2008

Keywords

• easy
• frac
• nonn

Comments

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

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

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

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

Crossrefs

Cf. A141244.