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A007244 McKay-Thompson series of class 3B for the Monster group.
(Formerly M5310)
4
1, 0, 54, -76, -243, 1188, -1384, -2916, 11934, -11580, -21870, 79704, -71022, -123444, 421308, -352544, -581013, 1885572, -1510236, -2388204, 7469928, -5777672, -8852004, 26869968, -20218587, -30177684, 89408826 (list; graph; refs; listen; history; text; internal format)
OFFSET
-1,3
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
N. D. Elkies, Elliptic and modular curves over finite fields and related computational issues, in AMS/IP Studies in Advanced Math., 7 (1998), 21-76, esp. p. 38.
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
J. McKay and H. Strauss, The q-series of monstrous moonshine and the decomposition of the head characters, Comm. Algebra 18 (1990), no. 1, 253-278.
FORMULA
G.f.: 12 + (eta(q)/eta(q^3))^12.
EXAMPLE
T3B = 1/q + 54*q - 76*q^2 - 243*q^3 + 1188*q^4 - 1384*q^5 - 2916*q^6 + ...
MATHEMATICA
a[ n_] := With[{m = n + 1}, SeriesCoefficient[ 12 q + (Product[ 1 - q^k, {k, m}] / Product[ 1 - q^k, {k, 3, m, 3}])^12, {q, 0, m}]] (* Michael Somos, Nov 08 2011 *)
QP = QPochhammer; s = 12 q + (QP[q]/QP[q^3])^12 + O[q]^30; CoefficientList[s, q] (* Jean-François Alcover, Nov 16 2015, adapted from PARI *)
PROG
(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( 12*x + (eta(x + A) / eta(x^3 + A))^12, n))} /* Michael Somos, Nov 08 2011 */
CROSSREFS
Essentially same as A030182, A045481.
Cf. A030182.
Sequence in context: A281920 A005129 A039532 * A365262 A114817 A045005
KEYWORD
sign,easy,nice
AUTHOR
STATUS
approved

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Last modified March 19 03:20 EDT 2024. Contains 370952 sequences. (Running on oeis4.)