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A143751
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McKay-Thompson series of class 60D for the Monster group with a(0) = -1.
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2
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1, -1, -1, 1, 0, 0, 0, -1, 1, 1, -1, -1, 1, 0, -1, 2, 0, -2, 2, -1, 0, 2, -4, 0, 5, -1, -4, 2, 1, -2, 3, -3, -2, 7, -5, -2, 8, -6, -5, 8, 1, -5, 2, -2, -1, 12, -11, -10, 21, -6, -10, 13, -7, -4, 11, -7, -4, 14, -13, -10, 33, -14, -28, 32, -3, -12, 18, -24, 1, 36, -27, -22, 44, -13, -35, 50, -13, -36, 46, -26, -6, 56, -63, -22, 89, -30
(list; graph; refs; listen; history; internal format)
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OFFSET
| -1,16
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LINKS
| M. Somos, A Remarkable eta-product Identity
Index entries for McKay-Thompson series for Monster simple group
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FORMULA
| Expansion of eta(q) * eta(q^12) * eta(q^15) * eta(q^20) / (eta(q^3) * eta(q^4) * eta(q^5) * eta(q^60)) in powers of q.
Expansion of F(q) * F(q^2) in powers of q^3 where F(q) is g.f. for A112215.
Euler transform of a period 60 sequence.
G.f. is a period 1 Fourier series which satisfies f(-1 / (60 t)) = 1 / 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^2 + v^2) * (1 + u + v) * (u + v + u*v) - u*v * (1+ 2*u + 2*v + u*v)^2.
G.f.: (x * Product_{k>0} P(30, x^k) * P(60, x^k))^(-1) where P(n, x) is the n-th cyclotomic polynomial.
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EXAMPLE
| 1/q - 1 - q + q^2 - q^6 + q^7 + q^8 - q^9 - q^10 + q^11 - q^13 + 2*q^14 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x + A) * eta(x^12 + A) * eta(x^15 + A) * eta(x^20 + A) / (eta(x^3 + A) * eta(x^4 + A) * eta(x^5 + A) * eta(x^60 + A)), n))}
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CROSSREFS
| Cf. A058728(n) = a(n) unless n=0. Convolution inverse of A143752.
Sequence in context: A099751 A159937 A058728 * A158950 A059581 A163542
Adjacent sequences: A143748 A143749 A143750 * A143752 A143753 A143754
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Aug 31 2008
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