A019450 Conjectured formula for irreducible 5-fold Euler sums of weight 2n+13.

1, 2, 5, 9, 15, 23, 36, 50, 71, 96, 127, 165, 213, 266, 333, 409, 498, 600, 720, 851, 1005, 1176, 1368, 1582, 1824, 2085, 2381, 2703, 3057, 3444, 3871, 4328, 4833, 5376, 5964, 6598, 7287, 8018, 8813, 9660, 10567, 11536, 12576, 13673, 14852, 16099, 17424, 18828

Offset

1,2

Comments

The conjectured formula has been verified by David Broadhurst up to a(12) = 165.

See D. J. Broadhurst link for definition and additional formulas. Perhaps this sequence should rather have offset 0? - Andrew Howroyd, Jan 01 2020

References

D. J. Broadhurst, Conjectural enumeration of irreducible MZV's: terashuffle tests at depth 4, up to weight 36, preprint, Oct 13 1996.

Links

Table of n, a(n) for n=1..48.

D. J. Broadhurst, Conjectured Enumeration of irreducible Multiple Zeta Values, from Knots and Feynman Diagrams, arXiv:hep-th/9612012, 1996.

Formula

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

Prog

(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

Crossrefs

Cf. A019449, A019459.

Sequence in context: A218914 A047809 A014126 * A098169 A055610 A134342

Adjacent sequences: A019447 A019448 A019449 * A019451 A019452 A019453

Keyword

nonn

Author

David Broadhurst

Status

approved