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

0,2

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).

Links

Table of n, a(n) for n=0..31.

Crossrefs

Cf. A141244.

Sequence in context: A200921 A135949 A168234 * A147032 A146261 A146176

Adjacent sequences: A141242 A141243 A141244 * A141246 A141247 A141248

Keyword

easy,frac,nonn

Author

Paul Barry, Jun 17 2008

Status

approved