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A244745 McKay-Thompson series of class 5A for the Monster group with a(0) = -6. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
-1,2
LINKS
FORMULA
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
EXAMPLE
G.f. = 1/q - 6 + 134*q + 760*q^2 + 3345*q^3 + 12256*q^4 + 39350*q^5 + ...
MATHEMATICA
a[ n_] := With[{A = (QPochhammer[ q] / QPochhammer[ q^5])^6 / q}, SeriesCoefficient[ A + 125 / A, {q, 0, n}]];
PROG
(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))};
CROSSREFS
Cf. A106248 ((eta(q) / eta(q^5))^6), A121591 ((eta(q^5) / eta(q))^6).
Sequence in context: A003373 A129047 A209276 * A179564 A263583 A295408
KEYWORD
sign
AUTHOR
Michael Somos, Jul 05 2014
STATUS
approved

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Last modified February 23 18:28 EST 2024. Contains 370283 sequences. (Running on oeis4.)