# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a001795 Showing 1-1 of 1 %I A001795 M4407 N1861 #43 Oct 23 2024 00:40:02 %S A001795 1,1,7,33,715,4199,52003,334305,17678835,119409675,1641030105, %T A001795 11435320455,322476036831,2295919134019,32968493968795, %U A001795 238436656380769,27767032438524099,203236010537432691,2989949596465113373 %N A001795 Coefficients of Legendre polynomials. %C A001795 Numerators in expansion of sqrt(c(x)), c(x) the g.f. of A000108. - _Paul Barry_, Jul 12 2005 %C A001795 Coefficient of Legendre_0(x) when x^n is written in term of Legendre polynomials. - _Michel Marcus_, May 28 2013 %D A001795 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). %D A001795 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A001795 T. D. Noe, Table of n, a(n) for n = 0..100 %H A001795 H. E. Salzer, Coefficients for expressing the first twenty-four powers in terms of the Legendre polynomials, Math. Comp., 3 (1948), 16-18. %F A001795 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 A001795 For n >= 1, 2^(n+1)*a(2^(n-1)) = A001791(2^n). - _Vladimir Shevelev_, Sep 05 2010 %F A001795 a(n) = numerator(binomial(2*n-1/2, n)/(2*n+1)). - _Tani Akinari_, Oct 22 2024 %o A001795 (PARI) my(x='x+O('x^30)); apply(numerator, Vec(((1-sqrt(1-4*x))/(2*x))^(1/2))) \\ _Michel Marcus_, Feb 04 2022 %o A001795 (PARI) a(n)=numerator(binomial(2*n-1/2, n)/(2*n+1)) \\ _Tani Akinari_, Oct 22 2024 %Y A001795 Divisor of A048990 and A065097. Apparently a bisection of A002596. %Y A001795 Bisection of A099024. %Y A001795 Cf. A000108, A001791. %K A001795 nonn %O A001795 0,3 %A A001795 _N. J. A. Sloane_ %E A001795 More terms from _Benoit Cloitre_, Mar 12 2002 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE