A019459 Conjectured formula for irreducible 6-fold Euler sums of weight 2n+16.

1, 3, 7, 14, 27, 45, 73, 113, 166, 239, 336, 458, 615, 814, 1055, 1354, 1717, 2149, 2666, 3281, 3994, 4834, 5808, 6927, 8214, 9692, 11359, 13261, 15405, 17812, 20512, 23540, 26892, 30635, 34776, 39347, 44387, 49945, 56015, 62688, 69971, 77910, 86553, 95966, 106140

Offset

1,2

Comments

The conjectured formula has been verified by David Broadhurst up to a(6) = 45.

See D. J. Broadhurst link for definition and additional formulas. Perhaps this sequence should rather have offset 0? - Andrew Howroyd, Jan 02 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..45.

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

Formula

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

Prog

(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

Crossrefs

Cf. A019449, A019450.

Sequence in context: A054355 A245268 A117071 * A276024 A274233 A369576

Adjacent sequences: A019456 A019457 A019458 * A019460 A019461 A019462

Keyword

nonn

Author

David Broadhurst

Status

approved