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 A045478 McKay-Thompson series of class 2A for Monster. 197
 1, 8, 4372, 96256, 1240002, 10698752, 74428120, 431529984, 2206741887, 10117578752, 42616961892, 166564106240, 611800208702, 2125795885056, 7040425608760, 22327393665024, 68134255043715, 200740384538624 (list; graph; refs; listen; history; text; internal format)
 OFFSET -1,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = -1..500 J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339. 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 a(n) ~ exp(2*Pi*sqrt(2*n)) / (2^(3/4)*n^(3/4)). - Vaclav Kotesovec, Apr 01 2017 Expansion of (1 + 32*A + (64*A)^2)/A, where A = (eta(q^2)/eta(q))^24, in powers of q. - G. C. Greubel, Jun 19 2018 MATHEMATICA nmax = 30; CoefficientList[Series[32*x + 4096*x^2*Product[(1 + x^k)^24, {k, 1, nmax}] + Product[1/(1 + x^k)^24, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 01 2017 *) eta[q_]:= q^(1/24)*QPochhammer[q]; A:= (eta[q^2]/eta[q])^24; a:= CoefficientList[Series[q*(1 + 32*A + 64^2*A^2)/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 19 2018 *) PROG (PARI) q='q+O('q^50); A = q*(eta(q^2)/eta(q))^24; Vec((1+32*A+(64*A)^2)/A) \\ G. C. Greubel, Jun 19 2018 CROSSREFS Cf. A007241, A007267. A045478, A007241, A106207, A007267, A101558 are all essentially the same sequence. Sequence in context: A306142 A317375 A100351 * A055319 A029736 A206460 Adjacent sequences:  A045475 A045476 A045477 * A045479 A045480 A045481 KEYWORD nonn,nice AUTHOR STATUS approved

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Last modified January 19 12:36 EST 2020. Contains 331049 sequences. (Running on oeis4.)