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A244745
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McKay-Thompson series of class 5A for the Monster group with a(0) = -6.
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2
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1, -6, 134, 760, 3345, 12256, 39350, 114096, 307060, 776000, 1867170, 4298600, 9540169, 20487360, 42756520, 86967184, 172859325, 336450560, 642489660, 1205572920, 2226005750, 4049168800, 7264172196, 12864273920, 22507811570, 38936117376, 66640520250
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OFFSET
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-1,2
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = -1..10000
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FORMULA
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Expansion of (eta(q) / eta(q^5))^6 + 125 * (eta(q^5) / eta(q))^6 in powers of q.
a(n) = A007251(n) = A045482(n) unless n = 0.
a(n) = A106248(n) + 125*A121591(n) for n > 0. - Seiichi Manyama, Mar 31 2017
a(n) ~ exp(4*Pi*sqrt(n/5)) / (sqrt(2)*5^(1/4)*n^(3/4)). - Vaclav Kotesovec, Apr 01 2017
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EXAMPLE
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G.f. = 1/q - 6 + 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 + 125 / A, {q, 0, n}]];
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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 + x^2 * 125 / A, n))};
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CROSSREFS
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Cf. A007251, A045482.
Cf. A106248 ((eta(q) / eta(q^5))^6), A121591 ((eta(q^5) / eta(q))^6).
Sequence in context: A003373 A129047 A209276 * A179564 A263583 A295408
Adjacent sequences: A244742 A244743 A244744 * A244746 A244747 A244748
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Jul 05 2014
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STATUS
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approved
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