OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from G. C. Greubel)
FORMULA
Expansion of (eta(q)^3 / eta(q^3))^4 in powers of q.
Euler transform of period 3 sequence [ -12, -12, -8, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (3 t)) = 729 (t/i)^4 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A033690.
G.f.: ( Product_{k>0} (1 - x^k)^3 / (1 - x^(3*k)) )^4.
EXAMPLE
G.f. = 1 - 12*q + 54*q^2 - 84*q^3 - 147*q^4 + 756*q^5 - 756*q^6 - 1212*q^7 + ...
MATHEMATICA
QP = QPochhammer; A133078[n_] := SeriesCoefficient[(QP[q]^3/QP[q^3])^4, {q, 0, n}]; Table[A133078[n], {n, 0, 50}] (* G. C. Greubel, Oct 20 2017 *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x*O(x^n); polcoeff( ( eta(x + A)^3 / eta(x^3 + A) )^4, n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Sep 08 2007
STATUS
approved