login
A261851
Decimal expansion of the central binomial sum S(7), where S(k) = Sum_{n>=1} 1/(n^k binomial(2n,n)).
2
5, 0, 1, 3, 2, 5, 8, 7, 2, 6, 8, 8, 1, 7, 8, 8, 0, 9, 4, 0, 2, 2, 9, 6, 7, 1, 0, 5, 5, 2, 7, 4, 9, 4, 4, 3, 7, 2, 6, 8, 7, 8, 3, 2, 9, 8, 5, 8, 0, 4, 5, 6, 8, 1, 5, 3, 6, 4, 5, 1, 2, 1, 7, 3, 3, 8, 8, 8, 7, 4, 1, 5, 8, 4, 5, 0, 6, 0, 6, 5, 3, 3, 0, 9, 0, 3, 1, 1, 3, 8, 8, 9, 7, 9, 4, 3, 9, 8, 9, 6, 1, 8, 1, 9, 4
OFFSET
0,1
LINKS
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 -6*Pi*Im(-PolyLog(6, (-1)^(1/3))) + (17*Pi^4*zeta(3))/1620 + (1/3)*Pi^2*zeta(5) - (493*zeta(7))/24.
EXAMPLE
0.501325872688178809402296710552749443726878329858...
MATHEMATICA
S[7]=-6*Pi*Im[-PolyLog[6, (-1)^(1/3)]] + (17*Pi^4*Zeta[3])/1620 + (1/3)*Pi^2*Zeta[5] - (493*Zeta[7])/24; RealDigits[S[7], 10, 105]//First
CROSSREFS
Cf. A073010 (S(1)), A086463 (S(2)), A145438 (S(3)), A086464 (S(4)), A261839 (S(5)), A261850 (S(6)), A261852 (S(8)).
Sequence in context: A104112 A115635 A019729 * A117015 A325736 A370012
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved