

A019450


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


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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:hepth/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



