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Search: id:A139381
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| A139381 |
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McKay-Thompson series of class 10E for the Monster group with a(0) = -3. |
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1
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| 1, -3, 1, 2, 2, -2, -1, 0, -4, -2, 5, 2, 0, 8, 2, -8, -3, -2, -14, -6, 14, 6, 4, 24, 12, -24, -11, -4, -40, -16, 38, 16, 5, 62, 24, -60, -24, -10, -94, -40, 91, 38, 18, 144, 62, -136, -57, -24, -214, -88, 201, 82, 30, 308, 122, -288, -117, -48, -440, -180, 410, 168, 74, 624, 262, -578, -238, -96, -874, -356, 804
(list; graph; listen)
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OFFSET
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-1,2
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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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Expansion of eta(q)^3 * eta(q^5) / eta(q^2) / eta(q^10)^3 in powers of q.
Expansion of q^(-1) * phi(-q) * f(-q) / (psi(q^5) * f(-q^10)) in powers of q where phi(), psi(), f() are Ramanujan theta functions.
Euler transform of period 10 sequence [ -3, -2, -3, -2, -4, -2, -3, -2, -3, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (10 t)) = 20 / f(t) where q = exp(2 pi i t).
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = (u + 4) * (20 + 6*v) - (v + 4) * (20 + v - u^2).
G.f.: (1 / x) * Product_{k>0} (1 - x^k)^3 * (1 - x^(5*k)) / ((1 - x^(2*k)) * (1 - x^(10*k))^3).
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EXAMPLE
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1/q - 3 + q + 2*q^2 + 2*q^3 - 2*q^4 - q^5 - 4*q^7 - 2*q^8 + 5*q^9 + ...
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PROGRAM
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(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x + A)^3 * eta(x^5 + A) / eta(x^2 + A) / eta(x^10 + A)^3, n))}
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CROSSREFS
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A058101(n) = a(n) unless n=0. Convolution inverse of A095846.
Cf. A138516. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 13 2008]
Sequence in context: A016568 A021888 A115310 this_sequence A038575 A033178 A029418
Adjacent sequences: A139378 A139379 A139380 this_sequence A139382 A139383 A139384
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Apr 15 2008
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