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A058664 McKay-Thompson series of class 40C for Monster. 2
1, 1, 2, 3, 4, 5, 8, 10, 13, 18, 22, 28, 36, 45, 56, 70, 85, 104, 128, 154, 187, 226, 270, 323, 386, 457, 542, 642, 755, 888, 1042, 1218, 1422, 1658, 1926, 2236, 2591, 2994, 3456, 3984, 4583, 5265, 6042, 6918, 7914, 9042, 10314, 11752, 13376, 15202, 17258, 19574, 22170, 25088, 28362, 32026, 36129, 40722, 45850 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

COMMENTS

Also McKay-Thompson series of class 40D for Monster.

LINKS

Seiichi Manyama, Table of n, a(n) for n = -1..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^8)*E(q^10))/(E(q^2)*E(q^40))/q where E(q) = prod(n>=1, 1 - q^n ), note that every second terms is zero and is omitted in this sequence, cf. the Pari/GP program. - Joerg Arndt, Apr 09 2016

a(n) ~ exp(sqrt(2*n/5)*Pi) / (2^(5/4)*5^(1/4)*n^(3/4)). - Vaclav Kotesovec, Apr 09 2016

EXAMPLE

T40C = 1/q + q + 2*q^3 + 3*q^5 + 4*q^7 + 5*q^9 + 8*q^11 + 10*q^13 + 13*q^15 + ...

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[(1-x^(4*k))*(1-x^(5*k))/((1-x^k)*(1-x^(20*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 09 2016 *)

eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/2)*( eta[q^4]*eta[q^5]/(eta[q]*eta[q^20])), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 14 2018 *)

PROG

(PARI) { N=66; q='q+O('q^N); my(E=eta); Vec( (E(q^4)*E(q^5))/(E(q^1)*E(q^20))/q ) } \\ Joerg Arndt, Apr 09 2016

CROSSREFS

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

Sequence in context: A223539 A211544 A080713 * A238479 A035562 A107234

Adjacent sequences:  A058661 A058662 A058663 * A058665 A058666 A058667

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from Joerg Arndt, Apr 09 2016

STATUS

approved

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Last modified January 17 06:41 EST 2019. Contains 319207 sequences. (Running on oeis4.)