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A007251
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McKay-Thompson series of class 5A for the Monster group.
(Formerly M5396)
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4
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1, 0, 134, 760, 3345, 12256, 39350, 114096, 307060, 776000, 1867170, 4298600, 9540169, 20487360, 42756520, 86967184, 172859325, 336450560, 642489660, 1205572920, 2226005750, 4049168800, 7264172196, 12864273920
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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 (eta(q) / eta(q^5))^6 + 6 + 125 * (eta(q^5) / eta(q))^6 in powers of q. - Michael Somos, Jul 05 2014
a(n) ~ exp(4*Pi*sqrt(n/5)) / (sqrt(2)*5^(1/4)*n^(3/4)). - Vaclav Kotesovec, Dec 04 2015
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EXAMPLE
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T5A = 1/q + 134*q + 760*q^2 + 3345*q^3 + 12256*q^4 + 39350*q^5 + ...
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MATHEMATICA
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a[ n_] := With[ {A = (QPochhammer[ q] / QPochhammer[ q^5])^6 / q}, SeriesCoefficient[ A + 6 + 125 / A, {q, 0, n}]]; (* Michael Somos, Jul 05 2014 *)
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PROG
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(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); A = (eta(x + A) / eta(x^5 + A))^6; polcoeff( A + 6*x + x^2 * 125 / A, n))}; /* Michael Somos, Jul 05 2014 */
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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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