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A244675 Decimal expansion of sum_(n>=1) (H(n)^3/(n+1)^3) where H(n) is the n-th harmonic number. 4
1, 7, 7, 5, 8, 6, 8, 8, 4, 2, 2, 6, 5, 9, 1, 1, 6, 8, 8, 2, 1, 0, 5, 2, 5, 5, 5, 4, 3, 3, 8, 0, 5, 4, 5, 2, 2, 3, 0, 0, 4, 1, 5, 0, 9, 1, 1, 0, 9, 4, 0, 7, 2, 3, 9, 4, 6, 6, 7, 3, 4, 6, 8, 3, 2, 8, 4, 5, 2, 8, 6, 1, 8, 3, 5, 5, 2, 7, 1, 8, 1, 7, 4, 5, 4, 7, 0, 9, 7, 8, 9, 8, 5, 2, 4, 5, 3, 8, 3, 9, 3, 6, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Philippe Flajolet, Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998) page 27.

FORMULA

Equals -11/120*Pi^4*zeta(3) + 1/3*Pi^2*zeta(5) + 119/16*zeta(7).

EXAMPLE

0.17758688422659116882105255543380545223004150911094072394667346832845...

MATHEMATICA

RealDigits[119/16*Zeta[7] - 33/4*Zeta[3]*Zeta[4] + 2*Zeta[2]*Zeta[5], 10, 103] // First

PROG

(PARI)  default(realprecision, 100);  -11/120*Pi^4*zeta(3) + 1/3*Pi^2*zeta(5) + 119/16*zeta(7) \\ G. C. Greubel, Aug 31 2018

(MAGMA) SetDefaultRealField(RealField(100)); R:= RealField(); L:=RiemannZeta(); -11/120*Pi(R)^4*Evaluate(L, 3) + 1/3*Pi(R)^2*Evaluate(L, 5) + 119/16*Evaluate(L, 7); // G. C. Greubel, Aug 31 2018

CROSSREFS

Cf. A001008, A002805, A002117, A013663, A013665, A244667, A244674.

Sequence in context: A154193 A278811 A021932 * A065472 A081112 A096151

Adjacent sequences:  A244672 A244673 A244674 * A244676 A244677 A244678

KEYWORD

nonn,cons,easy

AUTHOR

Jean-François Alcover, Jul 04 2014

STATUS

approved

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Last modified December 1 22:12 EST 2021. Contains 349435 sequences. (Running on oeis4.)