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A058594 McKay-Thompson series of class 25A for Monster. 1
1, 0, 4, 5, 10, 16, 25, 36, 55, 75, 110, 150, 209, 280, 385, 504, 675, 880, 1155, 1485, 1925, 2450, 3136, 3960, 5010, 6276, 7875, 9784, 12175, 15040, 18576, 22800, 27986, 34155, 41670, 50604, 61400, 74204, 89605, 107800, 129568, 155250, 185810, 221760, 264385 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

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, Commun. Algebra 22, No. 13, 5175-5193 (1994).

David A. Madore, Coefficients of Moonshine (McKay-Thompson) series, The Math Forum

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of A + 1 + 5/A, where A = eta(q)/eta(q^25), in powers of q. - G. C. Greubel, Jun 22 2018

a(n) ~ exp(4*Pi*sqrt(n)/5) / (sqrt(10) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T25A = 1/q + 4*q + 5*q^2 + 10*q^3 + 16*q^4 + 25*q^5 + 36*q^6 + 55*q^7 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q];  A:= (eta[q]/eta[q^25]); a:= CoefficientList[Series[1 + A + 5/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 22 2018 *)

PROG

(PARI) q='q+O('q^50); A = eta(q)/(q*eta(q^25)); Vec(A + 1 + 5/A) \\ G. C. Greubel, Jun 22 2018

CROSSREFS

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

Sequence in context: A118735 A002970 A073611 * A285289 A022309 A049897

Adjacent sequences:  A058591 A058592 A058593 * A058595 A058596 A058597

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from Michel Marcus, Feb 20 2014

STATUS

approved

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Last modified January 17 10:21 EST 2019. Contains 319218 sequences. (Running on oeis4.)