OFFSET
-1,2
LINKS
G. C. Greubel, Table of n, a(n) for n = -1..1000
M. Koike, Mathieu group M24 and modular forms, Nagoya Math. J., 99 (1985), 147-157. MR0805086 (87e:11060)
FORMULA
Associated with permutations in Mathieu group M24 of shape (4)^4(2)^2(1)^4.
G.f. is a period 1 Fourier series which satisfies f(-1 / (4 t)) = f(t) where q = exp(2 Pi i t).
a(n) ~ exp(2*Pi*sqrt(n)) / (2*n^(3/4)). - Vaclav Kotesovec, Sep 07 2017
EXAMPLE
G.f. = 1/q + 4 + 276*q + 2048*q^2 + 11202*q^3 + 49152*q^4 + 184024*q^5 + ...
MATHEMATICA
a[0] = 4; a[n_] := SeriesCoefficient[ Product[1 - q^k, {k, 1, n+1, 2}]^24/q, {q, 0, n}] // Abs; Table[a[n], {n, -1, 21}] (* Jean-François Alcover, Oct 14 2013, after Michael Somos *)
QP = QPochhammer; s = (QP[q^2]^2/QP[q]/QP[q^4])^24 - 20*q + O[q]^30; CoefficientList[s, q] (* Jean-François Alcover, Nov 15 2015, after Michael Somos *)
a[ n_] := SeriesCoefficient[ -20 + QPochhammer[ -q, q^2]^24 / q, {q, 0, n}]; (* Michael Somos, May 05 2016 *)
PROG
(PARI) {a(n) = my(A); if( n<-1, 0, A = x^2 * O(x^n); A = (eta(x + A) / eta(x^4 + A))^8 / x; polcoeff( 12 + A + 256 / A, n))};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Nov 22 2007
STATUS
approved