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A038360 Ranks of certain relations among Euler sums of weight n. 1


%S 1,3,6,14,29,60,123,249,503,1012,2032,4075,8164,16347,32719,65471,

%T 130986,262030,524137,1048376,2096887,4193953,8388143,16776600,

%U 33553616,67107783,134216296,268433559,536868399,1073738495,2147479238,4294961454,8589926853,17179858932,34359724787,68719458745,137438929639,274877875372

%N Ranks of certain relations among Euler sums of weight n.

%C It is conjectured that this is (apart from offset) the same as A216714.

%H P. Flajolet and B. Salvy, <a href="http://projecteuclid.org/euclid.em/1047674270">Euler sums and contour integral representations</a>, Experimental Mathematics, Vol. 7 Issue 1 (1998).

%H S. Saito, T. Tanaka, N. Wakabayashi, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Saito/saito22.html">Combinatorial Remarks on the Cyclic Sum Formula for Multiple Zeta Values </a>, J. Int. Seq. 14 (2011) # 11.2.4, Table 1.

%H M. Waldschmidt, <a href="http://www.math.jussieu.fr/~miw/articles/pdf/MZV2011IMSc.pdf">Lectures on Multiple Zeta Values</a> (IMSC2011).

%F a(n) = A000079(n-2) - A000931(n+3) [Saito]. - _R. J. Mathar_, Jul 22 2017

%t a[n_] := 2^(n-2) - SeriesCoefficient[(1-x^2)/(1-x^2-x^3), {x, 0, n+3}];

%t Table[a[n], {n, 3, 40}] (* _Jean-Fran├žois Alcover_, Jul 29 2018, after _R. J. Mathar_ *)

%K nonn

%O 3,2

%A _N. J. A. Sloane_

%E More terms from _Jean-Fran├žois Alcover_, Jul 29 2018

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Last modified April 15 13:37 EDT 2021. Contains 342977 sequences. (Running on oeis4.)