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

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

Table of n, a(n) for n=3..40.

Philippe Flajolet and Bruno Salvy, Euler sums and contour integral representations, Experimental Mathematics, Vol. 7 Issue 1 (1998).

Shingo Saito, Tatsushi Tanaka, and Noriko Wakabayashi, Combinatorial Remarks on the Cyclic Sum Formula for Multiple Zeta Values, J. Int. Seq. 14 (2011) # 11.2.4, Table 1.

Michel Waldschmidt, Lectures on Multiple Zeta Values (IMSC2011). [Wayback Machine link]

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

Adjacent sequences: A038357 A038358 A038359 * A038361 A038362 A038363

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Jean-François Alcover, Jul 29 2018

Status

approved