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Search: id:A134781
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| A134781 |
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McKay-Thompson series of class 23A for the Monster group with a(0) = 1. |
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1
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| 1, 1, 4, 7, 13, 19, 33, 47, 74, 106, 154, 214, 307, 417, 575, 772, 1045, 1379, 1837, 2394, 3135, 4048, 5232, 6686, 8560, 10840, 13737, 17273, 21701, 27086, 33783, 41890, 51893, 63969, 78748, 96536, 118196, 144146, 175561, 213122, 258327, 312202
(list; graph; listen)
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OFFSET
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-1,3
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REFERENCES
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M. Koike, Matheiu group M24 and modular forms, Nagoya Math. J., 99 (1985), 147-157. MR0805086 (87e:11060)
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FORMULA
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Associated with permutations in Mathieu group M24 of shape (23)(1).
G.f. is Fourier series of a level 23 modular function. f(-1/ (23 t)) = 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 - v^2) * (u^2 - v) + 2*(u*v * (u + v) + 2*(u^2 + v^2) + 5*u*v + 3*(u + v) + 1).
G.f. A(x) satisfies 0 = f(A(x), A(x^2), A(x^4)) where f(u, v, w) = v^2 * (2 - u - w) + v*(9 + 2*(u + w)) + u^2 + u*w + w^2 + 4*(u + w) + 6.
G.f.: (Sum_{j,k} x^(2*j^2 + j*k + 3*k^2)) / (x * Product_{k>0} (1 - x^k) * (1 - x^(23*k))).
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EXAMPLE
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1/q + 1 + 4*q + 7*q^2 + 13*q^3 + 19*q^4 + 33*q^5 + 47*q^6 + 74*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( (1 + 2 * x * Ser(qfrep([4, 1; 1, 6], n, 1))) / (eta(x + A) * eta(x^23 + A)), n))}
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CROSSREFS
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A058570(n) = a(n) unless n=0. Convolution with A030199 is A028930.
Sequence in context: A075315 A023496 A058570 this_sequence A100848 A051458 A068940
Adjacent sequences: A134778 A134779 A134780 this_sequence A134782 A134783 A134784
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Nov 12 2007
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