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%I #22 Oct 14 2019 11:44:50
%S 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,
%T -21,-4,30,-29,-4,41,-40,-7,55,-53,-8,75,-72,-12,98,-94,-14,130,-124,
%U -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
%N Coefficients of the C-Bailey Mod 9 identity.
%H Seiichi Manyama, <a href="/A104469/b104469.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+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
%F 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
%e G.f.: 1 - q + q^3 - q^4 + 2*q^6 - 2*q^7 - q^8 + 3*q^9 - 3*q^10 + ...
%o (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
%Y Cf. A104467, A104468.
%K sign,look
%O 0,7
%A _Eric W. Weisstein_, Mar 09 2005
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