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A058516 McKay-Thompson series of class 16C for Monster. 4
1, 0, 8, 16, 34, 64, 112, 192, 319, 512, 808, 1248, 1886, 2816, 4144, 6016, 8643, 12288, 17296, 24144, 33442, 45952, 62720, 85056, 114620, 153600, 204728, 271456, 358204, 470528, 615344, 801408, 1039621, 1343488, 1729920, 2219808, 2838920, 3619136, 4599664 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

COMMENTS

A058516, A176143, A214035, A215346 are all essentially the same sequence. - N. J. A. Sloane, Aug 08 2012

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

LINKS

Seiichi Manyama, Table of n, a(n) for n = -1..10000

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

a(n) ~ exp(sqrt(n)*Pi) / (2^(3/2) * n^(3/4)). - Vaclav Kotesovec, May 01 2017

Expansion of eta(q^4)^10/(eta(q)^2 *eta(q^2)^3 *eta(q^8)^3* eta(q^16)^2)) - 2 in powers of q. - G. C. Greubel, May 28 2018

Expansion of -2 + (1/q) * chi(q)^2 * chi(q^2)^7 * chi(q^4)^2 in powers of q where chi() is a Ramanujan theta function. - Michael Somos, Feb 09 2019

EXAMPLE

T16C = 1/q + 8*q + 16*q^2 + 34*q^3 + 64*q^4 + 112*q^5 + 192*q^6 + 319*q^7 + ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; A058516:= CoefficientList[Series[ q*(-2 + eta[q^4]^10/(eta[q]^2 *eta[q^2]^3 *eta[q^8]^3* eta[q^16]^2)), {q, 0, 60}], q]; Table[A058516[[n]], {n, 1, 50}] (* G. C. Greubel, May 28 2018 *)

a[ n_] := SeriesCoefficient[ -2 + q^-1 QPochhammer[ -q, q^2]^2 QPochhammer[ -q^2, q^4]^7 QPochhammer[ -q^4, q^8]^2, {q, 0, n}]; (* Michael Somos, Feb 09 2019 *)

PROG

(PARI) q='q+O('q^30); {h = (1/q)*(eta(q^4)^10/(eta(q)^2*eta(q^2)^3 *eta(q^8)^3*eta(q^16)^2))};  Vec(-2 + h) \\ G. C. Greubel, May 28 2018

CROSSREFS

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

Cf. A176143, A214035 (same sequence except for n=0).

Sequence in context: A043891 A072578 A271994 * A217672 A194601 A200271

Adjacent sequences:  A058513 A058514 A058515 * A058517 A058518 A058519

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from Michel Marcus, Feb 18 2014

STATUS

approved

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Last modified October 22 05:29 EDT 2019. Contains 328315 sequences. (Running on oeis4.)