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%I #10 Jan 02 2020 16:13:50
%S 1,3,7,14,27,45,73,113,166,239,336,458,615,814,1055,1354,1717,2149,
%T 2666,3281,3994,4834,5808,6927,8214,9692,11359,13261,15405,17812,
%U 20512,23540,26892,30635,34776,39347,44387,49945,56015,62688,69971,77910,86553,95966,106140
%N Conjectured formula for irreducible 6-fold Euler sums of weight 2n+16.
%C The conjectured formula has been verified by _David Broadhurst_ up to a(6) = 45.
%C See D. J. Broadhurst link for definition and additional formulas. Perhaps this sequence should rather have offset 0? - _Andrew Howroyd_, Jan 02 2020
%D D. J. Broadhurst, Conjectural enumeration of irreducible MZV's: terashuffle tests at depth 4, up to weight 36, preprint, Oct 13 1996.
%H D. J. Broadhurst, <a href="https://arxiv.org/abs/hep-th/9612012">Conjectured Enumeration of irreducible Multiple Zeta Values, from Knots and Feynman Diagrams</a>, arXiv:hep-th/9612012, 1996.
%F G.f.: (1 + 2*x + 3*x^2 + 4*x^3 + 6*x^4 + 6*x^5 + 6*x^6 + 7*x^7 + 4*x^8 + 5*x^9 + 4*x^10 + 2*x^11 + 2*x^12 - x^16 + x^17)/((1 - x)*(1 - x^2)*(1 - x^3)*(1 - x^4)*(1 - x^6)*(1 - x^9)). - _Andrew Howroyd_, Jan 01 2020
%o (PARI) Vec((1 + 2*x + 3*x^2 + 4*x^3 + 6*x^4 + 6*x^5 + 6*x^6 + 7*x^7 + 4*x^8 + 5*x^9 + 4*x^10 + 2*x^11 + 2*x^12 - x^16 + x^17)/((1 - x)*(1 - x^2)*(1 - x^3)*(1 - x^4)*(1 - x^6)*(1 - x^9)) + O(x^50)) \\ _Andrew Howroyd_, Jan 01 2020
%Y Cf. A019449, A019450.
%K nonn
%O 1,2
%A _David Broadhurst_
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