A104467 Coefficients of the A-Bailey Mod 9 identity.

1, 0, 0, 1, -1, -1, 2, -1, -1, 3, -2, -2, 5, -3, -3, 7, -5, -4, 11, -6, -6, 15, -10, -9, 22, -13, -12, 30, -19, -17, 42, -25, -23, 56, -35, -31, 77, -45, -41, 100, -62, -55, 133, -79, -71, 173, -105, -93, 226, -134, -120, 289, -175, -154, 373, -220, -196, 472, -284, -250, 601, -355, -314, 755, -451, -396, 950

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) * Product_{k=1..3*n} (1-x^k) / (Product_{k=1..n} (1-x^(3*k)) * Product_{k=1..2*n} (1-x^(3*k))). - Seiichi Manyama, Oct 14 2019

G.f.: Product_{k>0} (1-x^(9*k-4)) * (1-x^(9*k-5)) / ( (1-x^(9*k-3)) * (1-x^(9*k-6)) ). - Seiichi Manyama, Oct 14 2019

Example

G.f.: 1 + q^3 - q^4 - q^5 + 2*q^6 - q^7 - q^8 + 3*q^9 - 2*q^10 + ...

Prog

(PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, (1-x^(9*k-4))*(1-x^(9*k-5))/((1-x^(9*k-3))*(1-x^(9*k-6))))) \\ Seiichi Manyama, Oct 14 2019

Crossrefs

Cf. A104468, A104469.

Sequence in context: A226009 A132462 A161039 * A132463 A153901 A132844

Adjacent sequences: A104464 A104465 A104466 * A104468 A104469 A104470

Keyword

sign

Author

Eric W. Weisstein, Mar 09 2005

Status

approved