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A058513 McKay-Thompson series of class 15b for Monster. 5
1, 0, 3, 2, -3, 0, 0, 6, 6, -8, 6, 0, 16, 12, -9, 10, 0, 36, 21, -30, 18, 0, 63, 48, -53, 36, 0, 114, 78, -84, 67, 0, 210, 140, -159, 96, 0, 336, 237, -266, 183, 0, 553, 378, -396, 284, 0, 900, 595, -672, 435, 0, 1383, 948, -1031, 690, 0, 2116, 1419, -1524, 1062, 0, 3240, 2150, -2349, 1524 (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, Comm. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of T15b = 2 + (-5 + T25A*(B + 5/B))*(-A + B)*(1/( B*A))^2*(D^3/C)/q^3 in powers of q, where A = eta(q)/eta(q^25), B = eta(q^3)/ eta(q^75), C = (eta(q^3)*eta(q^5)/(eta(q)*eta(q^15)))^3, D = q*(eta(q^3) /eta(q^15))^2, and T25A = A + 5/A. - G. C. Greubel, Jun 21 2018

EXAMPLE

T15b = 1/q + 3*q + 2*q^2 - 3*q^3 + 6*q^6 + 6*q^7 - 8*q^8 + 6*q^9 + 16*q^11 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; nmax=66; A := (eta[q]/eta[q^25]); B := (eta[q^3]/eta[q^75]); c := (eta[q^3]*eta[q^5]/(eta[q]*eta[q^15]))^3; d := q*(eta[q^3]/eta[q^15])^2; T25A := A + 5/A; T15b := 2 + (-5 + T25A*(B + 5/B))*(-A + B)*(1/(B*A))^2*(d^3/c)/q^3; a:= CoefficientList[Series[ Simplify[q*T15b, q>0], {q, 0, nmax}], q]; Table[a[[n]], {n, 1, nmax}] (* G. C. Greubel, Jun 21 2018, fixed by Vaclav Kotesovec, Jul 03 2018 *)

PROG

(PARI) q='q+O('q^70); A=(eta(q)/eta(q^25))/q; B=eta(q^3)/(q^3*eta(q^75)); C = (eta(q^3)*eta(q^5)/(eta(q)*eta(q^15)))^3/q; D = (eta(q^3)/eta(q^15) )^2; T25A = A + 5/A; T15b = 2 + (-5 + T25A*(B + 5/B))*(-A + B)*(1/( B*A))^2*(D^3/C)/q^3; Vec(T15b) \\ G. C. Greubel, Jun 21 2018

CROSSREFS

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

Sequence in context: A108032 A053370 A016458 * A319650 A285736 A325142

Adjacent sequences:  A058510 A058511 A058512 * A058514 A058515 A058516

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(24) onward added by G. C. Greubel, Jun 21 2018

STATUS

approved

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Last modified October 15 00:14 EDT 2019. Contains 328025 sequences. (Running on oeis4.)