

A238182


Decimal expansion of sum_(n>=1) H(n)^2/n^4 where H(n) is the nth harmonic number (Quadratic Euler Sum S(2,4)).


3



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
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OFFSET

1,2


COMMENTS

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


LINKS

Table of n, a(n) for n=1..100.
Philippe Flajolet, Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998) page 24.


FORMULA

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


EXAMPLE

1.221879945319880138518806475290994812569...


MATHEMATICA

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


CROSSREFS

Cf. A152648, A152649, A152651, A218505, A238168, A238181, A238183.
Sequence in context: A121350 A198569 A135080 * A117260 A077944 A077992
Adjacent sequences: A238179 A238180 A238181 * A238183 A238184 A238185


KEYWORD

nonn,cons


AUTHOR

JeanFrançois Alcover, Feb 19 2014


STATUS

approved



