A022497 Conjectured number of irreducible multiple zeta values of depth 9 and weight 2n+25.

2, 7, 24, 59, 135, 276, 531, 955, 1656, 2740, 4401, 6855, 10421, 15466, 22536, 32207, 45320, 62814, 85916, 116023, 154977, 204759, 267964, 347472, 446809, 569937, 721743, 907503, 1133712, 1407519, 1737335

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (2, 2, -4, -4, 2, 10, -2, -11, 3, 6, 0, -7, 2, 8, -8, -2, 7, 0, -6, -3, 11, 2, -10, -2, 4, 4, -2, -2, 1).

Formula

G.f.: (2 + 3*x + 6*x^2 + 5*x^3 + 5*x^4 + 8*x^5 + 7*x^6 + 3*x^7 + 6*x^8 + 5*x^9 + 3*x^12 - 3*x^14 - 2*x^15 + 2*x^16 + 2*x^17 - x^18) / ((1-x)^2 * (1-x^2)^3 * (1-x^3)^2 * (1-x^6) * (1-x^9)).

Mathematica

CoefficientList[Series[(2+3x+6x^2+5x^3+5x^4+8x^5+7x^6+3x^7+6x^8+5x^9+3x^12-3x^14-2x^15+2x^16+2x^17-x^18)/((1-x)^2(1-x^2)^3(1-x^3)^2(1-x^6)(1-x^9)), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, 2, -4, -4, 2, 10, -2, -11, 3, 6, 0, -7, 2, 8, -8, -2, 7, 0, -6, -3, 11, 2, -10, -2, 4, 4, -2, -2, 1}, {2, 7, 24, 59, 135, 276, 531, 955, 1656, 2740, 4401, 6855, 10421, 15466, 22536, 32207, 45320, 62814, 85916, 116023, 154977, 204759, 267964, 347472, 446809, 569937, 721743, 907503, 1133712}, 50] (* Harvey P. Dale, Jun 12 2023 *)

Crossrefs

Sequence in context: A171130 A112089 A075062 * A358655 A258341 A054128

Adjacent sequences: A022494 A022495 A022496 * A022498 A022499 A022500

Keyword

nonn

Author

David Broadhurst

Status

approved