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A112197 McKay-Thompson series of class 56b for the Monster group. 1
1, 1, 1, -1, 1, 0, 2, -1, 2, 1, 3, -1, 4, 1, 4, 0, 5, 1, 7, -2, 8, 1, 10, -1, 12, 2, 14, -2, 17, 3, 21, -3, 24, 3, 28, -4, 34, 4, 39, -4, 46, 5, 53, -4, 61, 4, 71, -6, 82, 6, 94, -7, 108, 7, 124, -8, 142, 11, 162, -11, 185, 10, 210, -12, 238, 14, 271, -15, 306, 15, 345, -14, 390, 17, 439, -20, 494 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,7
LINKS
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
Expansion of A + q/A, where A = q^(1/2)*eta(q^4)*eta(q^14)/(eta(q^2)* eta(q^28)), in powers of q. - G. C. Greubel, Jul 01 2018
EXAMPLE
T56b = 1/q + q + q^3 - q^5 + q^7 + 2*q^11 - q^13 + 2*q^15 + q^17 + ...
MATHEMATICA
eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^4]*eta[q^14]/(eta[q^2]*eta[q^28])); a:= CoefficientList[Series[A + q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jul 01 2018 *)
PROG
(PARI) q='q+O('q^50); A = eta(q^4)*eta(q^14)/(eta(q^2)*eta(q^28)); Vec(A + q/A) \\ G. C. Greubel, Jul 01 2018
CROSSREFS
Sequence in context: A361734 A263111 A260438 * A112198 A326850 A303756
KEYWORD
sign
AUTHOR
Michael Somos, Aug 28 2005
STATUS
approved

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Last modified March 19 06:50 EDT 2024. Contains 370953 sequences. (Running on oeis4.)