A022498 Conjectured number of irreducible multiple zeta values of depth 10 and weight 2n+28.

2, 10, 34, 93, 222, 481, 970, 1837, 3312, 5734, 9569, 15492, 24410, 37550, 56531, 83511, 121200, 173169, 243848, 338857, 465113, 631300, 847803, 1127560, 1485938, 1941619, 2516688, 3237780, 4135821, 5247902, 6616867

Offset

0,1

Links

Table of n, a(n) for n=0..30.

Formula

G.f.: (2 + 8*x + 22*x^2 + 47*x^3 + 85*x^4 + 138*x^5 + 204*x^6 + 274*x^7 + 341*x^8 + 403*x^9 + 441*x^10 + 472*x^11+ 480*x^12 + 485*x^13 + 479*x^14 + 477*x^15 + 467*x^16 + 454*x^17 + 432*x^18+ 394*x^19 + 343*x^20 + 280*x^21 + 209*x^22 + 143*x^23 + 80*x^24 + 41*x^25 + 11*x^26+ 2*x^27 - 2*x^28 + 3*x^29 + 4*x^30 + 9*x^31 + 6*x^32 + 5*x^33 + 2*x^34 - x^37) / ((1-x) * (1-x^2) * (1-x^3)^2 * (1-x^4)^2 * (1-x^5) * (1-x^6)^2 * (1-x^15)).

Crossrefs

Sequence in context: A059924 A304159 A211905 * A036799 A190161 A196969

Adjacent sequences: A022495 A022496 A022497 * A022499 A022500 A022501

Keyword

nonn

Author

David Broadhurst

Status

approved