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A045482 McKay-Thompson series of class 5A for Monster. 3
1, 4, 134, 760, 3345, 12256, 39350, 114096, 307060, 776000, 1867170, 4298600, 9540169, 20487360, 42756520, 86967184, 172859325, 336450560, 642489660, 1205572920, 2226005750, 4049168800, 7264172196, 12864273920, 22507811570, 38936117376, 66640520250, 112915572144 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = -1..1000

J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.

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

J. McKay and H. Strauss, The q-series of monstrous moonshine and the decomposition of the head characters, Comm. Algebra 18 (1990), no. 1, 253-278.

Index entries for McKay-Thompson series for Monster simple group

FORMULA

a(n) ~ exp(4*Pi*sqrt(n/5)) / (sqrt(2)*5^(1/4)*n^(3/4)). - Vaclav Kotesovec, Apr 01 2017

Expansion of 10 + F +125/F, where F = (eta(q)/eta(q^5))^6, in powers of q. - G. C. Greubel, Jun 02 2018

MATHEMATICA

nmax = 30; CoefficientList[Series[10*x + 125*x^2*Product[((1 - x^(5*k))/(1 - x^k))^6, {k, 1, nmax}] + Product[((1 - x^k)/(1 - x^(5*k)))^6, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 01 2017 *)

eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[ q*(10 + (eta[q]/eta[q^5])^6 + 125*(eta[q^5]/eta[q])^6), {q, 0, 60}], q];

Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 02 2018 *)

CROSSREFS

Cf. A007251.

Sequence in context: A194539 A146547 A274703 * A263588 A006429 A016483

Adjacent sequences:  A045479 A045480 A045481 * A045483 A045484 A045485

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 23 03:06 EST 2019. Contains 319368 sequences. (Running on oeis4.)