OFFSET
-1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = -1..500
J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
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
a(n) ~ exp(2*Pi*sqrt(2*n)) / (2^(3/4)*n^(3/4)). - Vaclav Kotesovec, Apr 01 2017
Expansion of (1 + 32*A + (64*A)^2)/A, where A = (eta(q^2)/eta(q))^24, in powers of q. - G. C. Greubel, Jun 19 2018
MATHEMATICA
nmax = 30; CoefficientList[Series[32*x + 4096*x^2*Product[(1 + x^k)^24, {k, 1, nmax}] + Product[1/(1 + x^k)^24, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 01 2017 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; A:= (eta[q^2]/eta[q])^24; a:= CoefficientList[Series[q*(1 + 32*A + 64^2*A^2)/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 19 2018 *)
PROG
(PARI) q='q+O('q^50); A = q*(eta(q^2)/eta(q))^24; Vec((1+32*A+(64*A)^2)/A) \\ G. C. Greubel, Jun 19 2018
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
STATUS
approved