A257045 Denominators of Apéry's rational approximations p_n/q_n to zeta(3).

1, 5, 292, 52020, 9504288, 29484180000, 17168660000, 801669704780000, 35930841355360000, 1250077234358967840000, 36426677336311407264000, 11464402743063221545440000, 42860453128110714373355232000

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..358

Stéphane Fischler, Irrationalité de valeurs de zêta. Séminaire Bourbaki (2002-2003) Vol. 45, pp. 27-62 [in French]

Eric Weisstein's MathWorld, Apéry's Constant

Wikipedia, Apéry's constant

Formula

See Mathematica script.

Example

0, 6/5,  351/292,  62531/52020, 11424695/9504288, 35441662103/29484180000, ...
0, 1.2, 1.202..., 1.2020569...,   1.202056903...,        1.20205690316..., ...

Mathematica

p[n_] := Sum[Binomial[n+k, k]^2*Binomial[n, k]^2*(Sum[1/m^3, {m, 1, n}] + Sum[ (-1)^(m-1)/(2*m^3*Binomial[n, m]*Binomial[m+n, m]), {m, 1, k}]), {k, 0, n}]; q[n_] := Sum[Binomial[n+k, k]^2*Binomial[n, k]^2, {k, 0, n}]; Table[p[n]/q[n], {n, 0, 12}] // Denominator

Crossrefs

Cf. A002117, A005259, A059415, A059416.

Sequence in context: A337540 A354962 A227579 * A256422 A140016 A282967

Adjacent sequences: A257042 A257043 A257044 * A257046 A257047 A257048

Keyword

nonn,frac

Author

Jean-François Alcover, Apr 15 2015

Status

approved