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A058685 McKay-Thompson series of class 45a for Monster. 2
1, 0, -1, 1, 0, 1, 2, 0, 1, 2, 0, -1, 4, 0, 1, 4, 0, -1, 6, 0, -1, 7, 0, 2, 11, 0, 0, 12, 0, -2, 16, 0, 0, 19, 0, 1, 25, 0, -1, 29, 0, 2, 37, 0, 1, 44, 0, -5, 56, 0, 3, 65, 0, 2, 80, 0, -5, 94, 0, 4, 114, 0, -1, 133, 0, -4, 160, 0, 7, 187, 0, 0, 223, 0, -6, 258, 0, 3, 305, 0, 3, 353, 0, -6, 415, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,7

REFERENCES

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

LINKS

G. A. Edgar, Table of n, a(n) for n = -1..1000

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of eta(q^9)*eta(q^15) / (eta(q^3)*eta(q^45)) - eta(q^3)*eta(q^45) / (eta(q^9)*eta(q^15)) in powers of q. - G. A. Edgar, Mar 20 2017

EXAMPLE

T45a = 1/q - q + q^2 + q^4 + 2*q^5 + q^7 + 2*q^8 - q^10 + 4*q^11 + q^13 + ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q*eta[q^9]*eta[q^15]/(eta[q^3] *eta[q^45]); a := CoefficientList[Series[A - q^2/A , {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 14 2018 *)

PROG

(PARI) q='q+O('q^99); Vec(eta(q^9)*eta(q^15) / (eta(q^3)*eta(q^45)) - q^2 * eta(q^3)*eta(q^45) / (eta(q^9)*eta(q^15))) \\ Joerg Arndt, Mar 20 2017

CROSSREFS

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

Sequence in context: A229140 A280317 A283304 * A029300 A096397 A291969

Adjacent sequences:  A058682 A058683 A058684 * A058686 A058687 A058688

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from G. A. Edgar, Mar 20 2017

STATUS

approved

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Last modified January 17 18:33 EST 2019. Contains 319250 sequences. (Running on oeis4.)