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A156215 Expansion of (chi(q^3) / chi(q))^6 + q / (chi(q^3) / chi(q))^6 in powers of q where chi() is a Ramanujan theta function.

%I A156215 #9 Feb 16 2025 08:33:09
%S A156215 1,-5,27,-41,146,-243,510,-887,1755,-2728,5052,-7857,13157,-20253,
%T A156215 32805,-48680,76568,-112320,169814,-246263,365013,-519046,755632,
%U A156215 -1063368,1516404,-2112551,2972160,-4089098,5683166,-7750782,10633276,-14382932,19539387
%N A156215 Expansion of (chi(q^3) / chi(q))^6 + q / (chi(q^3) / chi(q))^6 in powers of q where chi() is a Ramanujan theta function.
%C A156215 Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%C A156215 Denoted by "(24~e)" in Simon Norton's replicable function list.
%H A156215 Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H A156215 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F A156215 Expansion of (chi(q) * chi(q^3))^3 - 8 * q / (chi(q) * chi(q^3))^3 in powers of q where chi() is a Ramanujan theta function.
%F A156215 G.f. is a period 1 Fourier series which satisfies f(-1 / (48 t)) = f(t) where q = exp(2 Pi i t).
%F A156215 a(n) = (-1)^n * A058490(n).
%e A156215 G.f. = 1 - 5*x + 27*x^2 - 41*x^3 + 146*x^4 - 243*x^5 + 5120*x^6 + ...
%e A156215 G.f. = 1/q - 5*q + 27*q^3 - 41*q^5 + 146*q^7 - 243*q^9 + 510*q^11 - 887*q^13 + ...
%o A156215 (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); A = ((eta(x^2 + A) * eta(x^6 + A))^2 / (eta(x + A) * eta(x^3 + A) * eta(x^4 + A) * eta(x^12 + A)))^3; polcoeff( A - 8 * x / A, n))};
%Y A156215 Cf. A058490.
%K A156215 sign
%O A156215 0,2
%A A156215 _Michael Somos_, Feb 06 2009