OFFSET
0,2
COMMENTS
REFERENCES
Max Koecher, Klassische elementare Analysis, Birkhäuser, Basel, Boston, 1987, p. 189.
LINKS
Robert Israel, Table of n, a(n) for n = 0..340
FORMULA
a(n) = numerators(s(n)) with the rationals (in lowest terms) s(n) = 1 + 2*Sum_{k=1..n} 1/(4*k^4 + 1), n >= 0.
EXAMPLE
The rationals s(n) begin: 1, 7/5, 93/65, 467/325, 19173/13325, 1170203/812825, 19898781/13818025, 2248887383/1561436825,...
s(10^5) = 1.4406595199775144260 (Maple 20 digits), to be compared with 1.4406595199775145926 (20 digits from A228048).
MAPLE
seq(numer(t), t=ListTools:-PartialSums([1, seq(2/(4*k^4+1), k=1..30)]));
MATHEMATICA
{1}~Join~Numerator[1 + 2 Accumulate[Array[1/(4 #^4 + 1) &, 17]]] (* Michael De Vlieger, Oct 30 2017 *)
PROG
(PARI) a(n) = numerator(1+2*sum(k=1, n, 1/(4*k^4 + 1))); \\ Michel Marcus, Oct 30 2017
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
Wolfdieter Lang, Oct 30 2017
STATUS
approved