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A058604 McKay-Thompson series of class 27d for Monster. 2
1, 2, -1, 0, 3, -2, 3, 4, 0, 4, 8, -4, 5, 12, -5, 8, 16, -6, 14, 28, -11, 14, 37, -16, 26, 50, -17, 36, 75, -30, 46, 100, -39, 64, 129, -48, 92, 184, -71, 108, 238, -94, 156, 308, -110, 202, 413, -160, 253, 530, -203, 332, 670, -248, 437, 880, -332, 528, 1107, -424, 696, 1388, -508, 876, 1773, -672, 1079, 2212, -831, 1362, 2735, -1012, 1717, 3446, -1288 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

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 (6 + T9b)^(1/3), where T9b = A112146, in powers of q^3. - G. C. Greubel, Jun 22 2018

EXAMPLE

T27d = 1/q + 2*q^2 - q^5 + 3*q^11 - 2*q^14 + 3*q^17 + 4*q^20 + 4*q^26 + ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q*(eta[q^3]/eta[q^9])^4; T9b := A + 9*q^2/A;  a:= CoefficientList[Series[(6*q^3 + (T9b /. {q -> q^3}) + O[q]^nmax)^(1/3), {q, 0, 300}], q]; Table[a[[n]], {n, 1, 120}][[1 ;; ;; 3]] (* G. C. Greubel, Jun 22 2018 *)

CROSSREFS

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

Sequence in context: A320839 A094314 A036864 * A072661 A103432 A103448

Adjacent sequences:  A058601 A058602 A058603 * A058605 A058606 A058607

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(8) onward added by G. C. Greubel, Jun 22 2018

STATUS

approved

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Last modified January 17 23:15 EST 2019. Contains 319251 sequences. (Running on oeis4.)