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A058632 McKay-Thompson series of class 32b for Monster. 1
1, 2, 3, 6, 7, 10, 16, 20, 29, 40, 52, 70, 91, 116, 149, 190, 242, 306, 383, 478, 590, 730, 897, 1096, 1342, 1630, 1975, 2390, 2873, 3448, 4133, 4932, 5880, 6994, 8290, 9814, 11587, 13650, 16058, 18848, 22089, 25842, 30178, 35186, 40950, 47594, 55231, 63996, 74068, 85592, 98776, 113864 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..1000

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

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of q^(1/4)*(eta(q^2)*eta(q^4)/(eta(q)*eta(q^8)))^2 in powers of q. -G. C. Greubel, Jun 23 2018

a(n) ~ exp(sqrt(n/2)*Pi) / (2^(7/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T32b = 1/q + 2*q^3 + 3*q^7 + 6*q^11 + 7*q^15 + 10*q^19 + 16*q^23 + 20*q^27 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; a := CoefficientList[Series[q^(1/4)*(eta[q^2]*eta[q^4]/(eta[q]*eta[q^8]))^2, {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* G. C. Greubel, Jun 23 2018 *)

PROG

(PARI) q='q+O('q^50); Vec((eta(q^2)*eta(q^4)/(eta(q)*eta(q^8)))^2) \\ G. C. Greubel, Jun 23 2018

CROSSREFS

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

Sequence in context: A288672 A086495 A051733 * A086583 A107852 A050031

Adjacent sequences:  A058629 A058630 A058631 * A058633 A058634 A058635

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(6) onward added by G. C. Greubel, Jun 23 2018

STATUS

approved

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Last modified January 22 09:52 EST 2019. Contains 319363 sequences. (Running on oeis4.)