This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A182034 #14 Feb 16 2025 08:33:13
%S A182034 1,-1,1,0,1,-2,0,0,1,0,-2,4,0,2,-8,0,1,2,0,-4,14,0,4,-24,0,1,6,0,-8,
%T A182034 38,0,8,-63,0,2,16,0,-14,92,0,14,-150,0,4,36,0,-24,208,0,23,-329,0,6,
%U A182034 78,0,-40,440,0,38,-684,0,10,160,0,-63,884,0,60,-1358,0
%N A182034 Expansion of c(q^2)^2 / (c(q) * c(q^3)) in powers of q where c() is a cubic AGM theta function.
%C A182034 Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%C A182034 Cubic AGM theta functions: a(q) (see A004016), b(q) (A005928), c(q) (A005882).
%H A182034 G. C. Greubel, <a href="/A182034/b182034.txt">Table of n, a(n) for n = 0..1000</a>
%H A182034 Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H A182034 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F A182034 Expansion of (chi(-q^3)^2 * psi(q^3)^4) / (psi(q) * f(-q^9)^3) in powers of q where psi(), chi(), f() are Ramanujan theta functions. - _Michael Somos_, May 20 2015
%F A182034 Expansion of eta(q) * eta(q^6)^6 / (eta(q^2)^2 * eta(q^3)^2 * eta(q^9)^3) in powers of q.
%F A182034 Euler transform of period 18 sequence [ -1, 1, 1, 1, -1, -3, -1, 1, 4, 1, -1, -3, -1, 1, 1, 1, -1, 0, ...].
%F A182034 a(n) = (-1)^n * A164615(n). a(3*n) = 0 unless n=0. a(3*n + 1) = - A092848(n). a(3*n + 2) = A216046(n).
%F A182034 Convolution inverse is A258100. - _Michael Somos_, May 20 2015
%e A182034 G.f. = 1 - q + q^2 + q^4 - 2*q^5 + q^8 - 2*q^10 + 4*q^11 + 2*q^13 - 8*q^14 + ...
%t A182034 a[ n_] := SeriesCoefficient[ (2 q^(1/8) QPochhammer[ q^6]^6) / (QPochhammer[ q^9]^3 EllipticTheta[ 2, 0, q^(1/2)] QPochhammer[ q^3]^2), {q, 0, n}]; (* _Michael Somos_, May 20 2015 *)
%t A182034 a[ n_] := SeriesCoefficient[ (QPochhammer[ q^3] EllipticTheta[ 2, 0, q^(3/2)]^3) / (4 q QPochhammer[ q^9]^3 EllipticTheta[ 2, 0, q^(1/2)]), {q, 0, n}]; (* _Michael Somos_, May 20 2015 *)
%o A182034 (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A) * eta(x^6 + A)^6 / (eta(x^2 + A)^2 * eta(x^3 + A)^2 * eta(x^9 + A)^3), n))};
%Y A182034 Cf. A092848, A164615, A216046, A258100.
%K A182034 sign
%O A182034 0,6
%A A182034 _Michael Somos_, Apr 07 2012