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%I M4407 N1861 #39 Feb 04 2022 07:43:00
%S 1,1,7,33,715,4199,52003,334305,17678835,119409675,1641030105,
%T 11435320455,322476036831,2295919134019,32968493968795,
%U 238436656380769,27767032438524099,203236010537432691,2989949596465113373
%N Coefficients of Legendre polynomials.
%C Numerators in expansion of sqrt(c(x)), c(x) the g.f. of A000108. - _Paul Barry_, Jul 12 2005
%C Coefficient of Legendre_0(x) when x^n is written in term of Legendre polynomials. - _Michel Marcus_, May 28 2013
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A001795/b001795.txt">Table of n, a(n) for n = 0..100</a>
%H H. E. Salzer, <a href="http://dx.doi.org/10.1090/S0025-5718-1948-0023123-5">Coefficients for expressing the first twenty-four powers in terms of the Legendre polynomials</a>, Math. Comp., 3 (1948), 16-18.
%F 1/(sqrt(1-x) + sqrt(1+x)) = Sum_{n>=0} (a(n)/b(n))*x^(2n) where b(n) is a power of 2. - _Benoit Cloitre_, Mar 12 2002
%F For n >= 1, 2^(n+1)*a(2^(n-1)) = A001791(2^n). - _Vladimir Shevelev_, Sep 05 2010
%o (PARI) my(x='x+O('x^30)); apply(numerator, Vec(((1-sqrt(1-4*x))/(2*x))^(1/2))) \\ _Michel Marcus_, Feb 04 2022
%Y Divisor of A048990 and A065097. Apparently a bisection of A002596.
%Y Bisection of A099024.
%Y Cf. A000108, A001791.
%K nonn
%O 0,3
%A _N. J. A. Sloane_
%E More terms from _Benoit Cloitre_, Mar 12 2002
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