

A045481


McKayThompson series of class 3B for the Monster group with a(0) = 3.


4



1, 3, 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

1,2


LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 1..1000
J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308339.
N. D. Elkies, Elliptic and modular curves over finite fields and related computational issues, in AMS/IP Studies in Advanced Math., 7 (1998), 2176, esp. p. 38.
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 51755193 (1994).
J. McKay and H. Strauss, The qseries of monstrous moonshine and the decomposition of the head characters, Comm. Algebra 18 (1990), no. 1, 253278.
Index entries for McKayThompson series for Monster simple group


FORMULA

Expansion of 9 + (eta(q) / eta(q^3))^12 in powers of q.


EXAMPLE

G.f. = 1/q  3 + 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[ 9 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 = 9*q+(QP[q]/QP[q^3])^12 + O[q]^30; CoefficientList[s, q] (* JeanFrançois Alcover, Nov 12 2015 *)


PROG

(PARI) {a(n) = my(A); if( n<1, 0, n++; A = x * O(x^n); polcoeff( 9*x + (eta(x + A) / eta(x^3 + A))^12, n))}; /* Michael Somos, Nov 08 2011 */


CROSSREFS

Essentially same as A007244, A030182, A045481.
Sequence in context: A208631 A093164 A092448 * A275566 A174782 A119294
Adjacent sequences: A045478 A045479 A045480 * A045482 A045483 A045484


KEYWORD

sign,easy,nice


AUTHOR

N. J. A. Sloane.


STATUS

approved



