|
%I #19 May 14 2020 21:47:56
%S 1,3,5,35,63,77,429,6435,12155,46189,88179,676039,1300075,5014575,
%T 215441,300540195,583401555,756261275,4418157975,6892326441,
%U 22427411435,263012370465,514589420475,895766768975,15801325804719,61989816618513,121683714103007
%N Denominators of the terms of Lehmer's series S_2(2), where S_k(x) = Sum_{n>=1} n^k*x^n/binomial(2*n, n).
%C The first 14 terms are identical to A052468.
%H F. J. Dyson, N. E. Frankel, M. L. Glasser, <a href="http://arxiv.org/abs/1009.4274">Lehmer's Interesting Series</a>, arXiv:1009.4274 [math-ph], 2010-2011.
%H F. J. Dyson, N. E. Frankel, and M. L. Glasser, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.120.02.116">Lehmer's interesting series</a>, Amer. Math. Monthly, 120 (2013), 116-130.
%H D. H. Lehmer, <a href="https://www.jstor.org/stable/2322496">Interesting series involving the central binomial coefficient</a>, Amer. Math. Monthly, 92(7) (1985), 449-457.
%F a(n) = denominator(n^2*2^n/C(2*n,n)).
%e 1/1, 8/3, 18/5, 128/35, 200/63, 192/77, 784/429, ... = A259852/A259853.
%t Table[2^n*n^2/Binomial[2*n, n] // Denominator, {n, 1, 40}]
%o (PARI) vector(40, n, denominator(n^2*2^n/binomial(2*n,n))) \\ _Michel Marcus_, Jul 07 2015
%Y Cf. A014307, A052468, A180875, A259852 (numerators).
%K nonn,frac,easy
%O 1,2
%A _Jean-François Alcover_, Jul 07 2015
|
