A238182 Decimal expansion of Sum_{n>=1} H(n)^2/n^4 where H(n) is the n-th harmonic number (Quadratic Euler Sum S(2,4)).

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

Offset: 1

Author

Jean-François Alcover, Feb 19 2014

Keywords

• nonn
• cons

Comments

No closed form of S(2,2q) is known to date, except for S(2,2) (A218505) and S(2,4) (this sequence).

Examples

			1.221879945319880138518806475290994812569...
		

Links

• Philippe Flajolet, Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998) page 24.

Crossrefs

Cf. A001008/A002805, A152648, A152649, A152651, A218505, A238168, A238181, A238183.

Programs

Mathematica

97/24*Zeta[6] - 2*Zeta[3]^2 // RealDigits[#, 10, 100]& // First

Formula

97/24*zeta(6) - 2*zeta(3)^2.