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%I #12 Jan 02 2020 00:34:31
%S 1,2,5,9,15,23,36,50,71,96,127,165,213,266,333,409,498,600,720,851,
%T 1005,1176,1368,1582,1824,2085,2381,2703,3057,3444,3871,4328,4833,
%U 5376,5964,6598,7287,8018,8813,9660,10567,11536,12576,13673,14852,16099,17424,18828
%N Conjectured formula for irreducible 5-fold Euler sums of weight 2n+13.
%C The conjectured formula has been verified by _David Broadhurst_ up to a(12) = 165.
%C See D. J. Broadhurst link for definition and additional formulas. Perhaps this sequence should rather have offset 0? - _Andrew Howroyd_, Jan 01 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.: x*(1 + 2*x + 3*x^2 + 3*x^3 + 2*x^4)/((1 - x^2)^2*(1 - x^3)^2*(1 - x^5)). - _Andrew Howroyd_, Jan 01 2020
%o (PARI) Vec((1 + 2*x + 3*x^2 + 3*x^3 + 2*x^4)/((1 - x^2)^2*(1 - x^3)^2*(1 - x^5)) + O(x^40)) \\ _Andrew Howroyd_, Jan 01 2020
%Y Cf. A019449, A019459.
%K nonn
%O 1,2
%A _David Broadhurst_