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A264595
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Let G[1](q) denote the g.f. for A003114 and G[2](q) the g.f. for A003106 (the two Rogers-Ramanujan identities). For i>=3, let G[i](q) = (G[i-1](q)-G[i-2](q))/q^(i-2). Sequence gives coefficients of G[8](q).
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9
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1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 9, 9, 11, 12, 14, 15, 18, 19, 22, 24, 27, 29, 33, 35, 40, 43, 48, 52, 59, 63, 71, 77, 86, 93, 104, 112, 125, 135, 149, 161, 179, 192, 212, 229, 252, 272, 299, 322, 354, 382, 418, 451, 494, 532, 581, 627, 683
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OFFSET
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0,19
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COMMENTS
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It is conjectured that G[i](q) = 1 + O(q^i) for all i.
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LINKS
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FORMULA
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a(n) ~ exp(2*Pi*sqrt(n/15)) / (2 * 3^(1/4) * sqrt(5) * phi^(13/2) * n^(3/4)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Dec 24 2016
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MATHEMATICA
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nmax = 100; CoefficientList[Series[Sum[x^(k*(k+7))/Product[1-x^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Dec 24 2016 *)
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CROSSREFS
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For the generalized Rogers-Ramanujan series G[1], G[2], G[3], G[4], G[5], G[6], G[7], G[8] see A003114, A003106, A006141, A264591, A264592, A264593, A264594, A264595.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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