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Search: id:A112331
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| A112331 |
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Number of monomial terms in expansion of n-th coefficient of replicable function as a polynomial in [c1,c2,c3,c4,c5,c7,c8,c9,c11,c17,c19,c23]. |
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+0
1
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| 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 1, 5, 16, 5, 6, 35, 1, 9, 1, 9, 10, 12, 1, 15, 107, 15, 479, 18, 578, 19, 965, 936, 27, 64, 21, 29, 2374, 72, 39, 32, 4527, 33, 6483, 43, 41, 129, 13942, 78, 18119, 127, 81, 71, 28481, 220, 66, 55, 123, 713, 70222, 85, 85970, 1155, 73, 123542
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OFFSET
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1,6
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COMMENT
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f(x)=1/x+c1*x+c2*x^2+c3*x^3+... is a replicable function if and only if H(a,b)=H(c,d) whenever a*b=c*d and gcd(a,b)=gcd(c,d) where H(,) is defined by Sum_{n,m>0} H(n,m) x^n y^m = log((1/x-1/y)/(f(x)-f(y))).
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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).
C. J. Cummins, T. Gannon, Modular equations and the genus zero property of moonshine functions, Invent. Math. 129 (1997), no. 3, 413-443. MR1465329 (98k:11046)
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EXAMPLE
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c6=c4+c2*c1 so a(6)=2, c10=c4+c4*c1+c3*c2+c2*c1 so a(10)=4. c12=c4+c4*c1+2*c3*c2+c2*c1^2+c2*c1 so a(12)=5.
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CROSSREFS
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Sequence in context: A010121 A139320 A118106 this_sequence A133910 A066441 A104404
Adjacent sequences: A112328 A112329 A112330 this_sequence A112332 A112333 A112334
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Sep 04 2005
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