This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A141244 #35 Apr 24 2023 09:45:31 %S A141244 0,0,1,1,5,5,11,11,93,93,193,193,793,793,1619,1619,26333,26333,53381, %T A141244 53381,215955,215955,436109,436109,3518265,3518265,7088533,7088533, %U A141244 28539857,28539857,57414019 %N A141244 Numerators in the expansion of (1-sqrt(1-x^2))/(1-x). %C A141244 The denominators in the expansion of (1-sqrt(1-x^2))/(1-x) are 1,1,2,2,8,8,16,16,... or 2^A005187(n) doubled. The sequence 0,1/2,1/2,5/8,5/8,... is the image of n 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 image of n+1 under this array is 1,1,1,.... %H A141244 G. C. Chingas, A. N. Garroway, W. B. Moniz, and R. D. Bertrand, <a href="https://doi.org/10.1021/ja00528a002">Adiabatic J cross-polarization in liquids for signal enhancement in NMR</a>, Journal of Chemical Physics, 102:8 (1980), 2526-2528 (page 1, equation (2)). %F A141244 a(2n) = a(2n+1) = A120778(n-1) (conjectural). - _Greg Martin_, Aug 16 2014, corrected by _M. F. Hasler_, Aug 18 2014 %o A141244 (PARI) a(n) = my(y=x+O(x^(n+1))); numerator(polcoeff((1-sqrt(1-y^2))/(1-y), n)); \\ _Michel Marcus_, Aug 17 2014 %Y A141244 Cf. A000108, A005187, A120778. %K A141244 easy,frac,nonn %O A141244 0,5 %A A141244 _Paul Barry_, Jun 17 2008