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Search: id:A097793
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| A097793 |
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G.f.: Product_{k>0} (1+x^k)/(1+x^(7k)). |
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+0
2
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| 1, 1, 1, 2, 2, 3, 4, 4, 5, 7, 8, 10, 12, 14, 17, 21, 24, 28, 34, 39, 46, 53, 61, 71, 82, 94, 108, 124, 142, 162, 185, 210, 238, 271, 306, 345, 390, 439, 494, 556, 623, 698, 783, 875, 977, 1092, 1216, 1354, 1508, 1674, 1859, 2064, 2286, 2532, 2803, 3098, 3424
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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McKay-Thompson series of class 56B for the Monster group.
Number of partitions of n into distinct parts not divisible by 7.
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REFERENCES
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D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
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FORMULA
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Euler transform of period 14 sequence [1,0,1,0,1,0,0,0,1,0,1,0,1,0,...].
Expansion of q^(1/4)eta(q^2)eta(q^7)/(eta(q)eta(q^14)) in powers of q.
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EXAMPLE
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T56B = 1/q + q^3 + q^7 + 2q^11 + 2q^15 + 3q^19 + 4q^23 + 4q^27 +...
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PROGRAM
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(PARI) a(n)=local(A); if(n<0, 0, A=x^n*O(x); polcoeff( prod(k=1, n, 1+x^k, 1+A)/ prod(k=1, n\7, 1+x^(7*k), 1+A), n))
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)*eta(x^7+A)/eta(x+A)/eta(x^14+A), n))}
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CROSSREFS
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Cf. A003105, A096938.
Adjacent sequences: A097790 A097791 A097792 this_sequence A097794 A097795 A097796
Sequence in context: A112582 A104648 A141271 this_sequence A015742 A015754 A113967
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Aug 24 2004
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