A112331 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].

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

Offset

1,6

Comments

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))).

References

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)

Links

Table of n, a(n) for n=1..64.

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).

Example

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.

Crossrefs

Sequence in context: A254048 A306671 A308210 * A133910 A345938 A066441

Adjacent sequences: A112328 A112329 A112330 * A112332 A112333 A112334

Keyword

nonn

Author

Michael Somos, Sep 04 2005

Status

approved