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A007264
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McKay-Thompson series of class 7A for Monster.
(Formerly M5302)
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4
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1, 0, 51, 204, 681, 1956, 5135, 12360, 28119, 60572, 125682, 251040, 487426, 920568, 1699611, 3070508, 5445510, 9490116, 16283793, 27537708, 45959775, 75760640, 123471327, 199081632, 317814988
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history;
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OFFSET
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-1,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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Expansion of (h+7)^2/h, where h = (eta(q)/eta(q^7))^4.
a(n) ~ exp(4*Pi*sqrt(n/7)) / (sqrt(2) * 7^(1/4) * n^(3/4)). - Vaclav Kotesovec, Dec 04 2015
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EXAMPLE
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T7A = 1/q + 51*q + 204*q^2 + 681*q^3 + 1956*q^4 + 5135*q^5 + 12360*q^6 + ...
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MATHEMATICA
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QP = QPochhammer; h = q*(QP[q^7]/QP[q])^4; s = 1 - 10*q + q*((1+7*h)^2/h - 1/q) + O[q]^30; CoefficientList[s, q] (* Jean-François Alcover, Nov 15 2015 *)
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PROG
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(PARI) q='q+O('q^50); F =(eta(q)/eta(q^7))^4/q; Vec(F*(1 + 7/F)^2 - 10) \\ G. C. Greubel, May 10 2018
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CROSSREFS
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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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