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A152651 Decimal expansion of 3*Zeta(5) - Zeta(3)*Pi^2/6. 10
1, 1, 3, 3, 4, 7, 8, 9, 1, 5, 1, 3, 2, 8, 1, 3, 6, 6, 0, 7, 9, 7, 0, 1, 1, 0, 1, 7, 8, 8, 5, 9, 7, 6, 9, 3, 2, 0, 8, 9, 0, 9, 1, 2, 9, 1, 8, 4, 5, 6, 0, 4, 2, 2, 7, 2, 2, 6, 7, 5, 5, 7, 5, 6, 6, 5, 6, 6, 9, 5, 7, 3, 5, 2, 1, 2, 2, 4, 0, 2, 4, 5, 9, 7, 7, 7, 4, 4, 9, 4, 7, 1, 4, 9, 6, 5, 0, 4, 0, 1, 7, 6, 6, 7, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
A division by 2 is missing in Mezo's penultimate formula on page 4.
LINKS
David Borwein and J. M. Borwein, On an intriguing integral and some series related to zeta(4), Proc. Am. Math. Soc. 123 (1995) 1191-1198.
Istvan Mezo, Summation of Hyperharmonic Numbers, arXiv:0811.0042 [math.CO], 2008.
FORMULA
Equals Sum_(j >= 1) H(j)/j^4 = where H(j) = A001008(j)/A002805(j).
Equals 3*A013663 - A002117*A013661.
EXAMPLE
Equals 1.1334789151328136607970110178859769320890912918456042272...
MATHEMATICA
RealDigits[3*Zeta[5]-Zeta[3]*Pi^2/6, 10, 120][[1]] (* Harvey P. Dale, Apr 29 2019 *)
PROG
(PARI) 3*zeta(5) - zeta(3)*Pi^2/6 \\ Michel Marcus, Jul 07 2015
CROSSREFS
Sequence in context: A051263 A058674 A349252 * A343396 A091973 A328798
KEYWORD
cons,easy,nonn
AUTHOR
R. J. Mathar, Dec 10 2008
STATUS
approved

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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)