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Search: id:A135213
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| A135213 |
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McKay-Thompson series of class 30G for the Monster group with a(0) = -1. |
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+0
2
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| 1, -1, 1, -1, 2, -2, 2, -3, 5, -5, 5, -7, 9, -10, 11, -14, 18, -20, 22, -27, 32, -36, 40, -48, 57, -63, 70, -82, 95, -106, 119, -137, 158, -175, 195, -222, 252, -280, 311, -352, 397, -439, 486, -546, 611, -676, 747, -834, 929, -1024, 1128, -1253, 1389, -1528, 1679, -1857, 2052, -2250, 2467, -2718, 2993
(list; graph; listen)
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OFFSET
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-1,5
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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 q^(-1) * psi(q^3) * psi(q^5) / (psi(q) * psi(q^15)) in powers of q where psi() is a Ramanujan theta function.
Expansion of eta(q) * eta(q^6)^2 * eta(q^10)^2 * eta(q^15) / (eta(q^2)^2 * eta(q^3) * eta(q^5) * eta(q^30)^2) in powers of q.
Euler transform of period 30 sequence [ -1, 1, 0, 1, 0, 0, -1, 1, 0, 0, -1, 0, -1, 1, 0, 1, -1, 0, -1, 0, 0, 1, -1, 0, 0, 1, 0, 1, -1, 0, ...].
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = (1 + v) * (v - u^2) - 2 * u * (v - u).
G.f. is a period 1 Fourier series which satisfies f(-1 / (30 t)) = g(t) where q = exp(2 pi i t) and g() is g.f. for A103259.
G.f.: 1 / ( x * Product_{k>0} P(15,x^k) * P(30,x^k)^2 ) where P(n,x) is the nth cyclotomic polynomial.
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EXAMPLE
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1/q - 1 + q - q^2 + 2*q^3 - 2*q^4 + 2*q^5 - 3*q^6 + 5*q^7 - 5*q^8 + ...
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PROGRAM
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(PARI) {a(n) = local(A); if( n<-1, 0, A = x^2 * O(x^n); polcoeff( eta(x + A) * eta(x^6 + A)^2 * eta(x^10 + A)^2 * eta(x^15 + A) / (eta(x^2 + A)^2 * eta(x^3 + A) * eta(x^5 + A) * eta(x^30 + A)^2) / x, n))}
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CROSSREFS
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A058618(n) = A133098(n) = a(n) unless n=0. Convolution inverse of A131794.
Sequence in context: A058618 A058727 A145725 this_sequence A035658 A077018 A007918
Adjacent sequences: A135210 A135211 A135212 this_sequence A135214 A135215 A135216
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Nov 23 2007
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