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A058686 McKay-Thompson series of class 45b for Monster. 3
1, 1, 2, 2, 4, 4, 6, 7, 11, 12, 16, 19, 25, 29, 37, 44, 56, 65, 80, 94, 114, 133, 160, 187, 223, 258, 305, 353, 415, 478, 560, 643, 749, 857, 993, 1134, 1308, 1490, 1712, 1946, 2227, 2525, 2880, 3259, 3706, 4186, 4747, 5350, 6050, 6806, 7677, 8620, 9702, 10875, 12212, 13664, 15315, 17107, 19136, 21342, 23834, 26540, 29585, 32896, 36613 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

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^9)*E(q^15))/(E(q^3)*E(q^45))/q where E(q) = Product_{n>=1} (1 - q^n), note that only every third term is nonzero and the zeros are omitted in this sequence, cf. the Pari/GP program. - Joerg Arndt, Apr 09 2016

a(n) ~ exp(4*Pi*sqrt(n/5)/3) / (5^(1/4)*sqrt(6)*n^(3/4)). - Vaclav Kotesovec, Apr 09 2016

Expansion of q^(1/3)*(eta(q^3)*eta(q^5)/(eta(q)*eta(q^15))) in powers of q. - G. C. Greubel, Jun 06 2018

EXAMPLE

T45b = 1/q + q^2 + 2*q^5 + 2*q^8 + 4*q^11 + 4*q^14 + 6*q^17 + 7*q^20 + ...

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[(1-x^(3*k))*(1-x^(5*k))/((1-x^k)*(1-x^(15*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 09 2016 *)

eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/3)*(eta[q^3]*eta[q^5]/(eta[q]*eta[q^15])), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 06 2018 *)

PROG

(PARI) { N=66; q='q+O('q^N); my(E=eta); Vec( (E(q^3)*E(q^5))/(E(q^1)*E(q^15))/q ) } \\ Joerg Arndt, Apr 09 2016

CROSSREFS

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

Sequence in context: A007212 A261797 A067590 * A027188 A089076 A123067

Adjacent sequences:  A058683 A058684 A058685 * A058687 A058688 A058689

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 20 02:13 EST 2019. Contains 319320 sequences. (Running on oeis4.)