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A258784 Denominators of a rational sequence related to the closed form evaluation of a Gaussian integer zeta sum. 1
5, 75, 4875, 82875, 6215625, 242409375, 19527421875, 44815433203125, 7185407790234375, 1699625304228515625, 22095128954970703125, 1538152402200285498046875, 1024661605286766357421875, 177310518163637910787353515625, 1171727007531373860453094482421875 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Jonathan Borwein, Also Eisenstein
FORMULA
p(1) = 1/5, p(n) = (3/((4n+1)*(2n-3)))*Sum_{k=1..n-1} p(k)*p(n-k).
The closed form of the Gaussian integer zeta sum in question is zeta_G(4n) = p(n)*L^(4n)/(4n-1), where L is the lemniscate constant.
EXAMPLE
Sequence of fractions begins:
1/5, 1/75, 2/4875, 1/82875, 2/6215625, 2/242409375, 4/19527421875, 223/ 44815433203125, ...
MATHEMATICA
p[1] = 1/5; p[n_] := p[n] = (3/((4n + 1)*(2n - 3)))*Sum[p[k]*p[n - k], {k, 1, n - 1}]; Table[p[n] // Denominator, {n, 1, 30}]
CROSSREFS
Cf. A062539 (lemniscate constant), A258783 (numerators).
Sequence in context: A238560 A303125 A332714 * A051481 A277296 A364323
KEYWORD
nonn,frac,easy
AUTHOR
STATUS
approved

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Last modified May 27 09:43 EDT 2024. Contains 372851 sequences. (Running on oeis4.)