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A093595
a(n) = numerator of Sum_{k in A030059} 1/k^(2n).
1
9, 15, 11340, 278775, 16247385, 37139825022300, 7581939039675, 76731473729479944375, 3915591422490399696806136375, 381397512477801513050979496875, 16227546388799797830522276658125
OFFSET
1,1
COMMENTS
See the Hardy reference, p. 65, fourth formula (with a misprint corrected), and the Weisstein link, eqs. (25)-(31). - Wolfdieter Lang, Oct 18 2016
REFERENCES
G. H. Hardy, Ramanujan, AMS Chelsea Publishing, 2002, pp. 64 - 65, (misprint on p.65, line starting with Hence: it should be ... -1/Zeta(s) not ... -Zeta(s)).
LINKS
Eric Weisstein's World of Mathematics, Prime Sums
FORMULA
Numerator of (zeta(2n)^2-zeta(4n))/(2zeta(2n)zeta(4n)).
EXAMPLE
9/(2*Pi^2), 15/(2*Pi^4), 11340/(691*Pi^6), 278775/(7234*Pi^8), ...
CROSSREFS
Cf. A030059, A093596 (denominators).
Sequence in context: A100241 A078794 A373332 * A330429 A372213 A215418
KEYWORD
nonn,easy,frac
AUTHOR
Eric W. Weisstein, Apr 03 2004
STATUS
approved