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%I #18 Apr 23 2018 09:33:53
%S 1,5,65,325,13325,812825,13818025,1561436825,45281667925,
%T 8195981894425,482116582025,434387040404525,135963143646616325,
%U 9925309486202991725,4178555293691459516225,154606545866584002100325,16852113499457656228935425,10330345575167543268337415525,1415257343797953427762225926925,1077010838630242558527053930389925
%N Denominators of partial sums of the series 1 + 2*Sum_{k >= 1} 1/(4*k^4 + 1).
%C The corresponding numerators are given in A292227.
%C For the value of the series see A292227, and the Koecher reference given there.
%H Robert Israel, <a href="/A292228/b292228.txt">Table of n, a(n) for n = 0..340</a>
%F 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.
%e See A292227.
%p seq(denom(t),t=ListTools:-PartialSums([1, seq(2/(4*k^4+1),k=1..30)])); # _Robert Israel_, Oct 30 2017
%t {1}~Join~Denominator[1 + 2 Accumulate[Array[1/(4 #^4 + 1) &, 19]]] (* _Michael De Vlieger_, Oct 30 2017 *)
%o (PARI) a(n) = denominator(1+2*sum(k=1, n, 1/(4*k^4 + 1))); \\ _Michel Marcus_, Oct 30 2017
%Y Cf. A292227.
%K nonn,frac,easy
%O 0,2
%A _Wolfdieter Lang_, Oct 30 2017
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