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A058531
McKay-Thompson series of class 18A for the Monster group.
4
1, 0, -2, 1, 0, 2, 1, 0, 0, -1, 0, -4, -1, 0, 4, 0, 0, 2, 1, 0, -8, 2, 0, 8, 0, 0, 2, -2, 0, -16, -3, 0, 16, -1, 0, 4, 4, 0, -28, 4, 0, 28, 1, 0, 8, -4, 0, -48, -6, 0, 46, -1, 0, 12, 5, 0, -80, 8, 0, 76, 1, 0, 20, -8, 0, -126, -10, 0, 120, -2, 0, 32, 11, 0, -196, 14, 0, 184, 4, 0, 48
OFFSET
-1,3
LINKS
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
a(3*n) = 0, a(3*n - 1) = A062242(n), a(3*n + 1) = -2*A092848(n). - Michael Somos, Mar 17 2004
Expansion of F - 2/F, where F = q^(1/3) * eta(q^2) * eta(q^3)^3 / (eta(q) * eta(q^6)^3), in powers of q. - G. C. Greubel, May 28 2018
EXAMPLE
T18A = 1/q - 2*q + q^2 + 2*q^4 + q^5 - q^8 - 4*q^10 - q^11 + 4*q^13 + 2*q^16 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ 1 + 1/q QPochhammer[ q] QPochhammer[ q^2] / (QPochhammer[ q^9] QPochhammer[ q^18]), {q, 0, n}]; (* Michael Somos, Apr 26 2015 *)
PROG
(PARI) {a(n) = my(A); if( n<1, n==-1, n++; A = x * O(x^n); polcoeff( eta(x + A) * eta(x^2 + A) / (eta(x^9 + A) * eta(x^18 + A)), n))}; /* Michael Somos, Mar 17 2004 */
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Nov 27 2000
STATUS
approved