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A058646
McKay-Thompson series of class 36C for Monster.
2
1, 1, 3, 2, 7, 6, 12, 10, 21, 22, 36, 36, 59, 63, 93, 98, 142, 156, 218, 238, 327, 358, 482, 528, 696, 769, 996, 1106, 1411, 1572, 1978, 2206, 2745, 3068, 3776, 4224, 5161, 5778, 6999, 7832, 9429, 10554, 12612, 14112, 16776, 18782, 22190, 24828, 29195, 32666, 38220, 42730, 49794, 55656, 64598, 72146, 83439, 93134, 107346
OFFSET
0,3
LINKS
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
G.f.: (E(q^6)*E(q^12))^2/(E(q^2)*E(q^4)*E(q^18)*E(q^36))/q where E(q) = prod(n>=1, 1 - q^n ), note that every second term is zero and has been omitted from this sequence, cf. the PARI/GP program. - Joerg Arndt, Apr 09 2016
a(n) ~ exp(2*Pi*sqrt(n)/3) / (2*sqrt(3)*n^(3/4)). - Vaclav Kotesovec, Sep 10 2015
EXAMPLE
T36C = 1/q + q + 3*q^3 + 2*q^5 + 7*q^7 + 6*q^9 + 12*q^11 + 10*q^13 + ...
MATHEMATICA
nmax = 50; CoefficientList[Series[Product[((1-x^(3*k)) * (1-x^(6*k)))^2 / ((1-x^k) * (1-x^(2*k)) * (1-x^(9*k)) * (1-x^(18*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 10 2015 *)
eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/2)*(eta[q^3]*eta[q^6])^2/(eta[q]*eta[q^2]*eta[q^9]*eta[q^18]), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 19 2018 *)
PROG
(PARI) { N=66; q='q+O('q^N); my(E=eta); Vec( (E(q^3)*E(q^6))^2 / (E(q^1)*E(q^2)*E(q^9)*E(q^18))/q ) } \\ Joerg Arndt, Apr 09 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
Offset corrected by N. J. A. Sloane, Feb 17 2014
More terms from Vaclav Kotesovec, Sep 10 2015
STATUS
approved