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A213617 Expansion of psi(x) * f(-x^3)^3 in powers of x where psi() and f() are Ramanujan theta functions.

%I A213617 #18 Feb 16 2025 08:33:17
%S A213617 1,2,3,3,3,5,4,5,4,5,7,5,8,4,5,8,8,9,5,7,9,6,9,9,7,10,10,11,5,6,12,12,
%T A213617 10,10,7,10,12,14,10,5,15,8,13,8,12,17,10,16,7,9,14,12,15,11,11,12,12,
%U A213617 16,14,15,13,15,13,7,12,17,16,15,10,13,18,16,20
%N A213617 Expansion of psi(x) * f(-x^3)^3 in powers of x where psi() and f() are Ramanujan theta functions.
%C A213617 Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H A213617 G. C. Greubel, <a href="/A213617/b213617.txt">Table of n, a(n) for n = 0..1000</a>
%H A213617 Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H A213617 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F A213617 Expansion of q^(-11/24) * eta(q^2)^2 * eta(q^3)^3 / eta(q)^2 in powers of q.
%F A213617 Euler transform of period 6 sequence [ 2, 0, -1, 0, 2, -3, ...].
%F A213617 6 * a(n) = A213618(24*n + 11).
%e A213617 G.f. = 1 + 2*x + 3*x^2 + 3*x^3 + 3*x^4 + 5*x^5 + 4*x^6 + 5*x^7 + 4*x^8 + 5*x^9 + ...
%e A213617 G.f. = q^11 + 2*q^35 + 3*q^59 + 3*q^83 + 3*q^107 + 5*q^131 + 4*q^155 + 5*q^179 + ...
%t A213617 a[ n_] := SeriesCoefficient[ QPochhammer[ x^2]^2 QPochhammer[ x^3]^3 / QPochhammer[x]^2, {x, 0, n}]; (* _Michael Somos_, Apr 26 2015 *)
%o A213617 (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^3 + A)^3 / eta(x + A)^2, n))};
%Y A213617 Cf. A213618.
%K A213617 nonn
%O A213617 0,2
%A A213617 _Michael Somos_, Jun 16 2012