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A038360
Ranks of certain relations among Euler sums of weight n.
1
1, 3, 6, 14, 29, 60, 123, 249, 503, 1012, 2032, 4075, 8164, 16347, 32719, 65471, 130986, 262030, 524137, 1048376, 2096887, 4193953, 8388143, 16776600, 33553616, 67107783, 134216296, 268433559, 536868399, 1073738495, 2147479238, 4294961454, 8589926853, 17179858932, 34359724787, 68719458745, 137438929639, 274877875372
OFFSET
3,2
COMMENTS
It is conjectured that this is (apart from offset) the same as A216714.
LINKS
P. Flajolet and B. Salvy, Euler sums and contour integral representations, Experimental Mathematics, Vol. 7 Issue 1 (1998).
S. Saito, T. Tanaka, N. Wakabayashi, Combinatorial Remarks on the Cyclic Sum Formula for Multiple Zeta Values , J. Int. Seq. 14 (2011) # 11.2.4, Table 1.
M. Waldschmidt, Lectures on Multiple Zeta Values (IMSC2011).
FORMULA
a(n) = A000079(n-2) - A000931(n+3) [Saito]. - R. J. Mathar, Jul 22 2017
MATHEMATICA
a[n_] := 2^(n-2) - SeriesCoefficient[(1-x^2)/(1-x^2-x^3), {x, 0, n+3}];
Table[a[n], {n, 3, 40}] (* Jean-François Alcover, Jul 29 2018, after R. J. Mathar *)
CROSSREFS
Sequence in context: A306884 A219768 A038359 * A216714 A084174 A036658
KEYWORD
nonn
EXTENSIONS
More terms from Jean-François Alcover, Jul 29 2018
STATUS
approved