A292228 Denominators of partial sums of the series 1 + 2*Sum_{k >= 1} 1/(4*k^4 + 1).

1, 5, 65, 325, 13325, 812825, 13818025, 1561436825, 45281667925, 8195981894425, 482116582025, 434387040404525, 135963143646616325, 9925309486202991725, 4178555293691459516225, 154606545866584002100325, 16852113499457656228935425, 10330345575167543268337415525, 1415257343797953427762225926925, 1077010838630242558527053930389925

Offset

0,2

Comments

The corresponding numerators are given in A292227.

For the value of the series see A292227, and the Koecher reference given there.

Links

Robert Israel, Table of n, a(n) for n = 0..340

Formula

a(n) = denominator(s(n)) with the rationals (in lowest terms) s(n) = 1 + 2*Sum_{k=1..n} 1/(4*k^4 + 1), n >= 0.

Example

See A292227.

Maple

seq(denom(t), t=ListTools:-PartialSums([1, seq(2/(4*k^4+1), k=1..30)])); # Robert Israel, Oct 30 2017

Mathematica

{1}~Join~Denominator[1 + 2 Accumulate[Array[1/(4 #^4 + 1) &, 19]]] (* Michael De Vlieger, Oct 30 2017 *)

Prog

(PARI) a(n) = denominator(1+2*sum(k=1, n, 1/(4*k^4 + 1))); \\ Michel Marcus, Oct 30 2017

Crossrefs

Cf. A292227.

Sequence in context: A211412 A052199 A093195 * A195579 A296369 A061184

Adjacent sequences: A292225 A292226 A292227 * A292229 A292230 A292231

Keyword

nonn,frac,easy

Author

Wolfdieter Lang, Oct 30 2017

Status

approved