A261850 Decimal expansion of the central binomial sum S(6), where S(k) = Sum_{n>=1} 1/(n^k binomial(2n,n)).

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

Offset

0,1

Links

Table of n, a(n) for n=0..104.

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) 7F6(1,1,1,1,1,1,1; 3/2,2,2,2,2,2; 1/4).

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

Example

0.50267652147826928645467745997934863966460260009164...

Mathematica

S[6] = Sum[1/(n^6*Binomial[2n, n]), {n, 1, Infinity}]; RealDigits[S[6], 10, 105]//First

Crossrefs

Cf. A073010 (S(1)), A086463 (S(2)), A145438 (S(3)), A086464 (S(4)), A261839 (S(5)), A261851 (S(7)), A261852 (S(8)).

Sequence in context: A199387 A195720 A198883 * A077496 A346120 A190913

Adjacent sequences: A261847 A261848 A261849 * A261851 A261852 A261853

Keyword

cons,easy,nonn

Author

Jean-François Alcover, Sep 03 2015

Status

approved