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A058623
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McKay-Thompson series of class 30b for Monster.
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1
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1, 0, 1, 2, 0, -2, 3, 0, 1, 6, 0, -2, 9, 0, 4, 12, 0, -2, 18, 0, 1, 26, 0, -4, 34, 0, 5, 48, 0, -4, 66, 0, 8, 86, 0, -12, 115, 0, 12, 152, 0, -14, 196, 0, 17, 252, 0, -16, 324, 0, 17, 410, 0, -24, 518, 0, 25, 652, 0, -28, 815, 0, 42, 1016, 0, -50, 1260, 0, 50, 1556, 0, -60, 1914, 0, 74, 2344, 0
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OFFSET
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-1,4
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LINKS
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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
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FORMULA
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Expansion of A + q^2/A, where A = q*(eta(q^6)*eta(q^15)/(eta(q^3) *eta(q^30)))^2, in powers of q. - G. C. Greubel, Jun 23 2018
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EXAMPLE
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T30b = 1/q + q + 2*q^2 - 2*q^4 + 3*q^5 + q^7 + 6*q^8 - 2*q^10 + 9*q^11 + ...
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MATHEMATICA
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nmax = 80; QP = QPochhammer; A = x^2*O[x]^(nmax+1); A = (QP[x^3 + A] * (QP[x^30 + A]/QP[x^6 + A]/QP[x^15 + A]))^2*x; a[n_] := SeriesCoefficient[ 1/A + A, n]; Table[a[n], {n, -1, nmax}] (* Jean-François Alcover, Nov 14 2015, adapted from PARI *)
eta[q_]:= q^(1/24)*QPochhammer[q]; A := q*(eta[q^6]*eta[q^15]/(eta[q^3]* eta[q^30]))^2; a:= CoefficientList[Series[A + q^2/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 23 2018 *)
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PROG
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(PARI) a(n)=local(A); if(n<-1, 0, A=x^2*O(x^n); A=(eta(x^3+A)*eta(x^30+A)/eta(x^6+A)/eta(x^15+A))^2*x; polcoeff(1/A+A, n)) \\ Michael Somos, May 02 2004
(PARI) q='q+O('q^80); A = (eta(q^6)*eta(q^15)/(eta(q^3) *eta(q^30)))^2; Vec(A+ q^2/A) \\ G. C. Greubel, Jun 23 2018
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CROSSREFS
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Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
Sequence in context: A344836 A323474 A132814 * A209689 A204329 A111565
Adjacent sequences: A058620 A058621 A058622 * A058624 A058625 A058626
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KEYWORD
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sign
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AUTHOR
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N. J. A. Sloane, Nov 27 2000
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STATUS
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approved
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