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A280666 Expansion of eta(q)^6/eta(q^6) in powers of q.

%I A280666 #15 Mar 25 2017 08:54:57
%S A280666 1,-6,9,10,-30,0,12,36,9,-60,-12,-54,62,120,18,-72,-102,-54,-36,156,
%T A280666 108,48,-192,-108,156,78,126,-206,-324,-72,240,324,225,-168,-276,-180,
%U A280666 132,264,72,-144,-588,-198,240,804,270,-288,-312,-324,206,486,225,-528
%N A280666 Expansion of eta(q)^6/eta(q^6) in powers of q.
%H A280666 Seiichi Manyama, <a href="/A280666/b280666.txt">Table of n, a(n) for n = 0..1000</a>
%F A280666 G.f.: Product_{n>0} (1-x^n)^6/(1-x^(6*n)).
%F A280666 Euler transform of period 6 sequence [ -6, -6, -6, -6, -6, -5, ...].
%p A280666 with(numtheory):
%p A280666 a:= proc(n) option remember; `if`(n=0, 1, add(add(d*
%p A280666       `if`(irem(d, 6)=0, -5, -6), d=divisors(j))*a(n-j), j=1..n)/n)
%p A280666     end:
%p A280666 seq(a(n), n=0..70);  # _Alois P. Heinz_, Jan 07 2017
%t A280666 QP = QPochhammer; QP[x]^6/QP[x^6] + O[x]^70 // CoefficientList[#, x]& (* _Jean-François Alcover_, Mar 25 2017 *)
%o A280666 (PARI) q='q+O('q^66); Vec( eta(q)^6/eta(q^6) ) \\ _Joerg Arndt_, Mar 25 2017
%Y A280666 Cf. A002448 (k=2), A005928 (k=3), A083703 (k=4), A109064 (k=5), this sequence (k=6), A160534 (k=7).
%K A280666 sign
%O A280666 0,2
%A A280666 _Seiichi Manyama_, Jan 07 2017