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

1,2

Comments

The first 14 terms are identical to A052468.

Links

Table of n, a(n) for n=1..27.

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.

Formula

a(n) = denominator(n^2*2^n/C(2*n,n)).

Example

1/1, 8/3, 18/5, 128/35, 200/63, 192/77, 784/429, ... = A259852/A259853.

Mathematica

Table[2^n*n^2/Binomial[2*n, n] // Denominator, {n, 1, 40}]

Prog

(PARI) vector(40, n, denominator(n^2*2^n/binomial(2*n, n))) \\ Michel Marcus, Jul 07 2015

Crossrefs

Cf. A014307, A052468, A180875, A259852 (numerators).

Sequence in context: A379507 A261659 A346715 * A052468 A055786 A001790

Adjacent sequences: A259850 A259851 A259852 * A259854 A259855 A259856

Keyword

nonn,frac,easy

Author

Jean-François Alcover, Jul 07 2015

Status

approved