A262178 Decimal expansion of Sum_{k>=0} (-1)^k/(3*k+1)^2.

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

Offset: 0

Author

Bruno Berselli, Sep 14 2015

Keywords

• nonn
• cons

Comments

Also, decimal expansion of Sum_{h>=0} Sum_{j=0..h} (-1)^j*binomial(h, j)/(4*(1 + h)*(1 + 6*j)*(2 + 3*j)).

Examples

			1 - 1/16 + 1/49 - 1/100 + 1/169 - 1/256 + 1/361 - 1/484 + ...
0.9515177134164150418664828314727415315447285082326970513300324315296113...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A006752.

Cf. A113476: Sum_{k>=0} (-1)^k/(3*k+1).

Cf. A226735: Sum_{k>=0} (-1)^k/(3*k+1)^3.

Programs

Mathematica

RealDigits[(Zeta[2, 1/6] - Zeta[2, 2/3])/36, 10, 100][[1]]

PARI

sumalt(k=0, (-1)^k/(3*k+1)^2) \\ Michel Marcus, Sep 14 2015

PARI

zetahurwitz(2,1/6)/36 - zetahurwitz(2,2/3)/36 \\ Charles R Greathouse IV, Jan 31 2018

Formula

Equals (zeta(2, 1/6) - zeta(2, 2/3))/36, where zeta(s,a) is the Hurwitz zeta function.