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%I #11 Mar 12 2021 22:24:46
%S 1,-1,-1,0,1,0,0,0,1,0,-2,0,0,2,0,0,1,0,0,-4,-2,0,4,0,0,1,2,0,-8,0,0,
%T 8,1,0,2,0,0,-14,-4,0,14,0,0,4,4,0,-24,0,0,23,1,0,6,0,0,-40,-8,0,38,0,
%U 0,10,8,0,-63,0,0,60,2,0,16,0,0,-98,-14,0,92
%N Expansion of chi(-q) * chi(-q^2) * chi(-q^6) * psi(q^6)^2 / (psi(q^9) * phi(-q^9)) in powers of q where phi(), psi(), chi() are Ramanujan theta functions.
%C Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H G. C. Greubel, <a href="/A182035/b182035.txt">Table of n, a(n) for n = 0..1000</a>
%H Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F Expansion of eta(q) * eta(q^12)^3 / (eta(q^4) * eta(q^6) * eta(q^9) * eta(q^18)) in powers of q.
%F Euler transform of period 36 sequence [ -1, -1, -1, 0, -1, 0, -1, 0, 0, -1, -1, -2, -1, -1, -1, 0, -1, 2, -1, 0, -1, -1, -1, -2, -1, -1, 0, 0, -1, 0, -1, 0, -1, -1, -1, 0, ...].
%F a(3*n) = 0 unless n=0. a(3*n + 1) = a(6*n + 2) = -A092848(n).
%e 1 - q - q^2 + q^4 + q^8 - 2*q^10 + 2*q^13 + q^16 - 4*q^19 - 2*q^20 + ...
%t eta[x_] := x^(1/24)*QPochhammer[x]; A182035[n_] := SeriesCoefficient[ eta[q]*eta[q^12]^3/(eta[q^4]*eta[q^6]*eta[q^9]*eta[q^18] ), {q, 0, n}];
%t Table[A182035[n], {n,0,50}] (* _G. C. Greubel_, Aug 21 2017 *)
%o (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A) * eta(x^12 + A)^3 / (eta(x^4 + A) * eta(x^6 + A) * eta(x^9 + A) * eta(x^18 + A)), n))}
%Y Cf. A092848
%K sign
%O 0,11
%A _Michael Somos_, Apr 07 2012
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