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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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A122336 A122355 A175433 * A323635 A125718 A268821
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

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Last modified March 19 06:32 EDT 2024. Contains 370953 sequences. (Running on oeis4.)