A104469 Coefficients of the C-Bailey Mod 9 identity.

1, -1, 0, 1, -1, 0, 2, -2, -1, 3, -3, 0, 5, -5, -1, 7, -7, -1, 11, -11, -2, 15, -15, -2, 22, -21, -4, 30, -29, -4, 41, -40, -7, 55, -53, -8, 75, -72, -12, 98, -94, -14, 130, -124, -21, 169, -161, -24, 220, -209, -34, 281, -267, -41, 362, -343, -55, 458, -433, -66, 582, -549, -88, 731, -689, -105, 918, -864, -137

Offset

0,7

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

J. Mc Laughlin, A. V. Sills and P. Zimmer, Rogers-Ramanujan-Slater Type Identities, Electronic J. Combinatorics, DS15, 1-59, May 31, 2008. See "2.9 Mod 9 Identities".

Eric Weisstein's World of Mathematics, Bailey Mod 9 Identities

Formula

G.f.: Sum_{n>=0} q^(3*n^2+3*n) * Product_{k=1..3*n+1} (1-x^k) / (Product_{k=1..n} (1-x^(3*k)) * Product_{k=1..2*n+1} (1-x^(3*k))). - Seiichi Manyama, Oct 14 2019

G.f.: Product_{k>0} (1-x^(9*k-1)) * (1-x^(9*k-8)) / ( (1-x^(9*k-3)) * (1-x^(9*k-6)) ). - Seiichi Manyama, Oct 14 2019

Example

G.f.: 1 - q + q^3 - q^4 + 2*q^6 - 2*q^7 - q^8 + 3*q^9 - 3*q^10 + ...

Prog

(PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, (1-x^(9*k-1))*(1-x^(9*k-8))/((1-x^(9*k-3))*(1-x^(9*k-6))))) \\ Seiichi Manyama, Oct 14 2019

Crossrefs

Cf. A104467, A104468.

Sequence in context: A145141 A103360 A267409 * A372437 A144112 A178568

Adjacent sequences: A104466 A104467 A104468 * A104470 A104471 A104472

Keyword

sign,look

Author

Eric W. Weisstein, Mar 09 2005

Status

approved