A259853 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).
1, 3, 5, 35, 63, 77, 429, 6435, 12155, 46189, 88179, 676039, 1300075, 5014575, 215441, 300540195, 583401555, 756261275, 4418157975, 6892326441, 22427411435, 263012370465, 514589420475, 895766768975, 15801325804719, 61989816618513, 121683714103007
Offset: 1
Examples
1/1, 8/3, 18/5, 128/35, 200/63, 192/77, 784/429, ... = A259852/A259853.
Links
- F. J. Dyson, N. E. Frankel, M. L. Glasser, Lehmer's Interesting Series, arXiv:1009.4274 [math-ph], 2010-2011.
- F. J. Dyson, N. E. Frankel, and M. L. Glasser, Lehmer's interesting series, Amer. Math. Monthly, 120 (2013), 116-130.
- D. H. Lehmer, Interesting series involving the central binomial coefficient, Amer. Math. Monthly, 92(7) (1985), 449-457.
Programs
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Mathematica
Table[2^n*n^2/Binomial[2*n, n] // Denominator, {n, 1, 40}] -
PARI
vector(40, n, denominator(n^2*2^n/binomial(2*n,n))) \\ Michel Marcus, Jul 07 2015
Formula
a(n) = denominator(n^2*2^n/C(2*n,n)).
Comments