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
Examples
See A292227.
Links
- Robert Israel, Table of n, a(n) for n = 0..340
Crossrefs
Cf. A292227.
Programs
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Maple
seq(denom(t),t=ListTools:-PartialSums([1, seq(2/(4*k^4+1),k=1..30)])); # Robert Israel, Oct 30 2017
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Mathematica
{1}~Join~Denominator[1 + 2 Accumulate[Array[1/(4 #^4 + 1) &, 19]]] (* Michael De Vlieger, Oct 30 2017 *) -
PARI
a(n) = denominator(1+2*sum(k=1, n, 1/(4*k^4 + 1))); \\ Michel Marcus, Oct 30 2017
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.
Comments