OFFSET
-1,3
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Seiichi Manyama, Table of n, a(n) for n = -1..10000
J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
N. D. Elkies, Elliptic and modular curves over finite fields and related computational issues, in AMS/IP Studies in Advanced Math., 7 (1998), 21-76, esp. p. 39.
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
J. McKay and H. Strauss, The q-series of monstrous moonshine and the decomposition of the head characters, Comm. Algebra 18 (1990), no. 1, 253-278.
FORMULA
Expansion of (h+7)^2/h, where h = (eta(q)/eta(q^7))^4.
a(n) ~ exp(4*Pi*sqrt(n/7)) / (sqrt(2) * 7^(1/4) * n^(3/4)). - Vaclav Kotesovec, Dec 04 2015
EXAMPLE
T7A = 1/q + 51*q + 204*q^2 + 681*q^3 + 1956*q^4 + 5135*q^5 + 12360*q^6 + ...
MATHEMATICA
QP = QPochhammer; h = q*(QP[q^7]/QP[q])^4; s = 1 - 10*q + q*((1+7*h)^2/h - 1/q) + O[q]^30; CoefficientList[s, q] (* Jean-François Alcover, Nov 15 2015 *)
PROG
(PARI) q='q+O('q^50); F =(eta(q)/eta(q^7))^4/q; Vec(F*(1 + 7/F)^2 - 10) \\ G. C. Greubel, May 10 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved