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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

G. C. Greubel, Table of n, a(n) for n = 0..1000

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

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

Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.

Sequence in context: A122336 A122355 A175433 * A125718 A268821 A014841

Adjacent sequences:  A058643 A058644 A058645 * A058647 A058648 A058649

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 January 21 19:08 EST 2019. Contains 319350 sequences. (Running on oeis4.)