The On-Line Encyclopedia of Integer Sequences (OEIS)

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A238168

Decimal expansion of sum_(n>=1) H(n)^2/n^5 where H(n) is the n-th harmonic number.
(history; published version)

#9 by Susanna Cuyler at Sat Dec 30 17:26:35 EST 2017

STATUS

proposed

approved

#8 by G. C. Greubel at Sat Dec 30 16:39:51 EST 2017

STATUS

editing

proposed

#7 by G. C. Greubel at Sat Dec 30 16:39:22 EST 2017

LINKS

G. C. Greubel, <a href="/A238168/b238168.txt">Table of n, a(n) for n = 1..10000</a>

FORMULA

Equals 6*zeta(7) - zeta(2)*zeta(5) - 5/2*zeta(3)*zeta(4).

MATHEMATICA

RealDigits[6*Zeta[7] - Zeta[2]*Zeta[5] - (5/2)*Zeta[3]*Zeta[4] // RealDigits[#, , 10, 100]& // First[[1]]

PROG

(PARI) 6*zeta(7) - zeta(2)*zeta(5) - (5/2)*zeta(3)*zeta(4) \\ G. C. Greubel, Dec 30 2017

STATUS

approved

editing

Discussion

Sat Dec 30

16:39

G. C. Greubel: Updated Mma code

#6 by Michel Marcus at Wed Feb 19 05:05:15 EST 2014

STATUS

editing

approved

#5 by Michel Marcus at Wed Feb 19 05:05:11 EST 2014

FORMULA

6*zeta(7) - zeta(2)*zeta(5) - 5/2*zeta(3)*zeta(4).

STATUS

reviewed

editing

#4 by Joerg Arndt at Wed Feb 19 04:28:45 EST 2014

STATUS

proposed

reviewed

#3 by Jean-François Alcover at Wed Feb 19 04:09:07 EST 2014

STATUS

editing

proposed

#2 by Jean-François Alcover at Wed Feb 19 04:05:10 EST 2014

NAME

allocated for JeanDecimal expansion of sum_(n>=1) H(n)^2/n^5 where H(n) is the n-François Alcoverth harmonic number.

DATA

1, 0, 9, 1, 8, 8, 2, 5, 8, 8, 6, 6, 4, 5, 3, 0, 0, 8, 5, 1, 6, 5, 7, 8, 2, 1, 3, 0, 6, 9, 9, 2, 7, 3, 8, 7, 3, 3, 7, 7, 5, 6, 7, 8, 8, 9, 5, 3, 2, 4, 0, 8, 6, 2, 6, 3, 8, 1, 2, 6, 6, 6, 6, 7, 4, 7, 6, 6, 6, 6, 7, 7, 6, 8, 4, 0, 1, 2, 8, 5, 8, 2, 0, 4, 3, 6, 9, 1, 8, 0, 6, 7, 4, 2, 6, 5, 7, 5, 7, 8

OFFSET

1,3

LINKS

Philippe Flajolet, Bruno Salvy, <a href="http://algo.inria.fr/flajolet/Publications/FlSa98.pdf">Euler Sums and Contour Integral Representations</a>, Experimental Mathematics 7:1 (1998) page 16.

FORMULA

6*zeta(7) - zeta(2)*zeta(5) - 5/2*zeta(3)*zeta(4)

EXAMPLE

1.091882588664530085165782130699273873...

MATHEMATICA

6*Zeta[7] - Zeta[2]*Zeta[5] - 5/2*Zeta[3]*Zeta[4] // RealDigits[#, 10, 100]& // First

CROSSREFS

Cf. A152648, A152649, A152651, A238166, A238167, A238169.

KEYWORD

allocated

nonn,cons

AUTHOR

Jean-François Alcover, Feb 19 2014

STATUS

approved

editing

#1 by Jean-François Alcover at Wed Feb 19 03:51:50 EST 2014

NAME

allocated for Jean-François Alcover

KEYWORD

allocated

STATUS

approved