A238169 Decimal expansion of sum_(n>=1) H(n)^3/n^4 where H(n) is the n-th harmonic number.

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

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Philippe Flajolet, Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998) page 16.

Formula

Equals (231/16)*Zeta(7) - (51/4)*Zeta(3)*Zeta(4) + 2*Zeta(2)*Zeta(5).

Example

1.38146831050385237300478512040662269993...

Mathematica

RealDigits[(231/16)*Zeta[7] - (51/4)*Zeta[3]*Zeta[4] + 2*Zeta[2]*Zeta[5], 10, 100][[1]] (* G. C. Greubel, Dec 30 2017 *)

Prog

(PARI) (231/16)*zeta(7) - (51/4)*zeta(3)*zeta(4) + 2*zeta(2)*zeta(5) \\ G. C. Greubel, Dec 30 2017

Crossrefs

Cf. A152648, A152649, A152651, A238166, A238167, A238168.

Sequence in context: A084185 A073227 A016550 * A341414 A086245 A247392

Adjacent sequences: A238166 A238167 A238168 * A238170 A238171 A238172

Keyword

nonn,cons

Author

Jean-François Alcover, Feb 19 2014

Status

approved