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Search: id:A107635
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| A107635 |
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McKay-Thompson series of class 32a for the Monster group. |
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+0
1
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| 1, 3, 3, 4, 9, 12, 15, 21, 30, 43, 54, 69, 94, 123, 153, 193, 252, 318, 391, 486, 609, 754, 918, 1119, 1376, 1680, 2019, 2432, 2946, 3540, 4220, 5034, 6015, 7157, 8463, 9999, 11835, 13956, 16374, 19206, 22542, 26376, 30750, 35829, 41745, 48526, 56250
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
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LINKS
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Index entries for McKay-Thompson series for Monster simple group
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FORMULA
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Given g.f. A(x), then B(x)=A(x^8)/x satisfies 0=f(B(x), B(x^3)) where f(u, v)=u^4+v^4+8*u*v-u^3*v^3.
Euler transform of period 4 sequence [3, -3, 3, 0, ...].
G.f.: Product_{k>0} (1+(-x)^k)^-3.
Expansion of q^(1/8)(eta(q^2)^2/(eta(q)eta(q^4)))^3 in powers of q.
Expansion of chi(q)^3 in powers of q where chi() is a Ramanujan theta function.
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EXAMPLE
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T32a = 1/q +3*q^7 +3*q^15 +4*q^23 +9*q^31 +12*q^39 +15*q^47 +...
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PROGRAM
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(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( (eta(x^2+A)^2/eta(x+A)/eta(x^4+A))^3, n))}
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CROSSREFS
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Cf. A022598(n)=(-1)^n*a(n).
Sequence in context: A045794 A065678 A022598 this_sequence A132319 A130626 A115284
Adjacent sequences: A107632 A107633 A107634 this_sequence A107636 A107637 A107638
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, May 18 2005
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