A058531 - OEIS

A058531

McKay-Thompson series of class 18A for the Monster group.

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

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OFFSET

-1,3

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, Commun. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

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

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

Cf. A062242, A092848.

Sequence in context: A093201 A067613 A264034 * A093073 A251635 A156319

Adjacent sequences: A058528 A058529 A058530 * A058532 A058533 A058534

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Nov 27 2000

STATUS

approved