login
A058648
McKay-Thompson series of class 36a for Monster.
1
1, -1, 0, 2, 2, 0, 3, -1, 0, 4, 0, 0, 5, 0, 0, 8, 2, 0, 11, -4, 0, 16, 4, 0, 21, -4, 0, 26, 2, 0, 34, -1, 0, 44, 4, 0, 58, -9, 0, 74, 12, 0, 93, -9, 0, 116, 4, 0, 143, -5, 0, 178, 12, 0, 221, -20, 0, 272, 24, 0, 332, -20, 0, 402, 14, 0, 487, -13, 0, 588, 24, 0, 710, -42, 0, 854, 50, 0
OFFSET
-1,4
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^6)*eta(q^9)/( eta(q^3)* eta(q^18)))^2, in powers of q. - G. C. Greubel, Jun 23 2018
EXAMPLE
T36a = 1/q - q + 2*q^5 + 2*q^7 + 3*q^11 - q^13 + 4*q^17 + 5*q^23 + 8*q^29 + ...
MATHEMATICA
eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^6]*eta[q^9]/( eta[q^3]*eta[q^18]))^2; a := CoefficientList[Series[ A -q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 23 2018 *)
PROG
(PARI) q='q+O('q^50); A = (eta(q^6)*eta(q^9)/(eta(q^3)*eta(q^18)))^2; Vec(A - q/A) \\ G. C. Greubel, Jun 23 2018
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
Terms a(12) onward added by G. C. Greubel, Jun 23 2018
STATUS
approved