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%I #24 Oct 20 2019 03:11:11
%S 1,-1,1,-1,2,-2,2,-3,4,-4,5,-6,8,-9,10,-12,15,-17,19,-22,27,-30,34,
%T -39,46,-52,58,-66,77,-86,96,-109,125,-139,155,-174,198,-220,244,-273,
%U 308,-341,377,-420,470,-519,573,-635,707,-779,857,-946,1049,-1152,1264,-1392,1536,-1683,1843,-2022,2224
%N Coefficients of the C-Rogers-Selberg identity.
%H Seiichi Manyama, <a href="/A104410/b104410.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from G. C. Greubel)
%H Vaclav Kotesovec, <a href="https://arxiv.org/abs/1509.08708">A method of finding the asymptotics of q-series based on the convolution of generating functions</a>, arXiv:1509.08708 [math.CO], 2015-2016.
%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 "2.7 The Rogers-Selberg Mod 7 Identities".
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Rogers-SelbergIdentities.html">Rogers-Selberg Identities</a>
%F Expansion of f(-q, -q^6) / f(-q^2) in powers of q where f() is Ramanujan's theta function.
%F Euler transform of period 14 sequence [ -1, 1, 0, 1, 0, 0, -1, 0, 0, 1, 0, 1, -1, 0, ...]. - _Michael Somos_, Dec 04 2007
%F a(n) ~ (-1)^n * cos(Pi/14) * 11^(1/4) * exp(Pi*sqrt(11*n/42)) / (3^(1/4) * 14^(3/4) * n^(3/4)). - _Vaclav Kotesovec_, Oct 04 2015
%e 1 - q + q^2 - q^3 + 2*q^4 - 2*q^5 + 2*q^6 - 3*q^7 + 4*q^8 - 4*q^9 + 5*q^10 + ...
%t nmax=60; CoefficientList[Series[Product[(1-x^(7*k-1))*(1-x^(7*k-6))*(1-x^(7*k))/(1-x^(2*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Oct 04 2015 *)
%o (PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1 - x^k + x*O(x^n))^[0, 1, -1, 0, -1, 0, 0, 1, 0, 0, -1, 0, -1, 1][k%14+1]), n))} /* _Michael Somos_, Dec 04 2007 */
%Y Cf. A104408, A104409.
%K sign
%O 0,5
%A _Eric W. Weisstein_, Mar 06 2005
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