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Search: id:A152944
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| A152944 |
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McKay-Thompson series of class 17A for the Monster group with a(0) = 2. |
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+0
2
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| 1, 2, 7, 14, 29, 50, 92, 148, 246, 386, 603, 904, 1367, 1996, 2914, 4160, 5924, 8290, 11581, 15942, 21878, 29712, 40184, 53876, 71979, 95436, 126097, 165556, 216594, 281848, 365548, 471808, 607050, 777794, 993528, 1264338, 1604434, 2029026
(list; graph; listen)
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OFFSET
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-1,2
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FORMULA
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Expansion of q^(-1) * ((psi(q^2) * phi(q^17) - q^4 * phi(q) * psi(q^34)) / (f(-q) * f(-q^17)))^2 in powers of q where phi(), psi(), f() are Ramanujan theta functions.
Expansion of q^(-1) * (F(q) - q^4 / F(q))^2 / (chi(-q) * chi(-q^17))^4 in powers of q where F(q) = G(q^17) / G(q), G(q) = chi(q) * chi(-q^2) and chi() is a Ramanujan theta function.
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = u*v * (1 - u^2/v) * (1 - v^2/u) - 4 * (1 + u + v) * (u + v + u*v).
G.f. is a period 1 Fourier series which satisfies f(-1 / (17 t)) = f(t) where q = exp(2 pi i t).
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EXAMPLE
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1/q + 2 + 7*q + 14*q^2 + 29*q^3 + 50*q^4 + 92*q^5 + 148*q^6 + 246*q^7 + ...
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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^4 + A)^2 * eta(x^34 + A)^5 / (eta(x + A) * eta(x^2 + A) * eta(x^17 + A)^3 * eta(x^68 + A)^2) - x^4 * eta(x^2 + A)^5 * eta(x^68 + A)^2 / (eta(x + A)^3 * eta(x^4 + A)^2 * eta(x^17 + A) * eta(x^34 + A)))^2, n))}
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CROSSREFS
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A058530(n) = a(n) unless n = 0. Convolution square of A058639.
Sequence in context: A068040 A005998 A122751 this_sequence A018437 A120739 A034791
Adjacent sequences: A152941 A152942 A152943 this_sequence A152945 A152946 A152947
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Dec 15 2008
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