A261852 Decimal expansion of the central binomial sum S(8), where S(k) = Sum_{n>=1} 1/(n^k binomial(2n,n)).

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

Offset

0,1

Links

Table of n, a(n) for n=0..99.

J. M. Borwein, D. J. Broadhurst, J. Kamnitzer, Central Binomial Sums, Multiple Clausen Values and Zeta Values, arXiv:hep-th/0004153, 2000.

Eric Weisstein's MathWorld, Central Binomial Coefficient

Formula

Equals (1/2) 8F7(1,...,1; 3/2,2,...,2; 1/4).

Also equals (4/45)*Integral_{0..Pi/3} t*log(2*sin(t/2))^6 dt.

Example

0.5006588912976705433145571270829868383840732523404540388886438...

Mathematica

S[8] = Sum[1/(n^8*Binomial[2n, n]), {n, 1, Infinity}]; RealDigits[S[8], 10, 100] // First

Crossrefs

Cf. A073010 (S(1)), A086463 (S(2)), A145438 (S(3)), A086464 (S(4)), A261839 (S(5)), A261850 (S(6)), A261851 (S(7)).

Sequence in context: A099223 A233427 A237660 * A254293 A263496 A308224

Adjacent sequences: A261849 A261850 A261851 * A261853 A261854 A261855

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 03 2015

Status

approved