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 A045481 McKay-Thompson 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) 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 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] (* Jean-François 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: A093164 A092448 A344424 * A275566 A068380 A174782 Adjacent sequences:  A045478 A045479 A045480 * A045482 A045483 A045484 KEYWORD sign,easy,nice AUTHOR STATUS approved

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Last modified August 1 14:14 EDT 2021. Contains 346391 sequences. (Running on oeis4.)