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A181977 Expansion of b(q) * c(q^3)^2 / 9 in powers of q where b(), c() are cubic AGM theta functions. 1

%I

%S 1,-3,0,8,-9,0,17,-27,0,40,-39,0,50,-72,0,96,-81,0,104,-150,0,176,

%T -153,0,170,-243,0,280,-216,0,273,-360,0,400,-351,0,362,-510,0,560,

%U -450,0,520,-648,0,736,-615,0,601,-864,0,936,-729,0,850,-1086,0,1160

%N Expansion of b(q) * c(q^3)^2 / 9 in powers of q where b(), c() are cubic AGM theta functions.

%C Cubic AGM theta functions: a(q) (see A004016), b(q) (A005928), c(q) (A005882).

%H G. C. Greubel, <a href="/A181977/b181977.txt">Table of n, a(n) for n = 2..2500</a>

%F Expansion of (eta(q) * eta(q^9)^2 / eta(q^3))^3 in powers of q.

%F Euler transform of period 9 sequence [-3, -3, 0, -3, -3, 0, -3, -3, -6, ...].

%F a(3*n + 1) = 0. a(3*n) = -3 * A106402(n).

%e G.f. = q^2 - 3*q^3 + 8*q^5 - 9*q^6 + 17*q^8 - 27*q^9 + 40*q^11 - 39*q^12 + ...

%t eta[q_]:= q^(1/24)*QPochhammer[q]; CoefficientList[Series[(eta[q]* eta[q^9]^2/eta[q^3])^3, {q, 0, 50}], q] (* _G. C. Greubel_, Aug 11 2018 *)

%o (PARI) {a(n) = my(A); if( n<2, 0, n = n-2; A = x * O(x^n); polcoeff( (eta(x + A) * eta(x^9 + A)^2 / eta(x^3 + A))^3, n))};

%Y Cf. A106402.

%K sign

%O 2,2

%A _Michael Somos_, Apr 04 2012

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Last modified March 2 09:56 EST 2021. Contains 341746 sequences. (Running on oeis4.)