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A104467 Coefficients of the A-Bailey Mod 9 identity. 3

%I

%S 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,

%T -13,-12,30,-19,-17,42,-25,-23,56,-35,-31,77,-45,-41,100,-62,-55,133,

%U -79,-71,173,-105,-93,226,-134,-120,289,-175,-154,373,-220,-196,472,-284,-250,601,-355,-314,755,-451,-396,950

%N Coefficients of the A-Bailey Mod 9 identity.

%H Seiichi Manyama, <a href="/A104467/b104467.txt">Table of n, a(n) for n = 0..10000</a>

%H J. Mc Laughlin, A. V. Sills and P. Zimmer, <a href="https://www.combinatorics.org/ojs/index.php/eljc/article/view/DS15">Rogers-Ramanujan-Slater Type Identities</a>, Electronic J. Combinatorics, DS15, 1-59, May 31, 2008. See "2.9 Mod 9 Identities".

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BaileyMod9Identities.html">Bailey Mod 9 Identities</a>

%F 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

%F 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

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

%o (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

%Y Cf. A104468, A104469.

%K sign

%O 0,7

%A _Eric W. Weisstein_, Mar 09 2005

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Last modified June 19 18:35 EDT 2021. Contains 345144 sequences. (Running on oeis4.)