cp's OEIS Frontend

A260167 Expansion of psi(x^4) * f(-x^3)^3 / chi(-x)^2 in powers of x where psi(), chi(), f() are Ramanujan theta functions.

%I A260167 #13 Feb 16 2025 08:33:26
%S A260167 1,2,3,3,4,7,7,8,7,10,11,10,13,11,15,16,19,18,14,20,21,20,21,21,25,22,
%T A260167 27,31,23,30,31,35,28,27,35,36,37,38,32,34,41,39,43,35,49,46,43,48,42,
%U A260167 55,51,49,50,38,55,52,57,63,47,60,54,62,63,51,65,66,67
%N A260167 Expansion of psi(x^4) * f(-x^3)^3 / chi(-x)^2 in powers of x where psi(), chi(), f() are Ramanujan theta functions.
%C A260167 Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H A260167 G. C. Greubel, <a href="/A260167/b260167.txt">Table of n, a(n) for n = 0..1000</a>
%H A260167 Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H A260167 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F A260167 Expansion of q^(-23/24) * eta(q^2)^2 * eta(q^3)^3 * eta(q^8)^2 / (eta(q)^2 * eta(q^4)) in powers of q.
%F A260167 Euler transform of period 24 sequence [ 2, 0, -1, 1, 2, -3, 2, -1, -1, 0, 2, -2, 2, 0, -1, -1, 2, -3, 2, 1, -1, 0, 2, -4, ...].
%F A260167 6 * a(n) = A260158(4*n + 3).
%e A260167 G.f. = 1 + 2*x + 3*x^2 + 3*x^3 + 4*x^4 + 7*x^5 + 7*x^6 + 8*x^7 + 7*x^8 + ...
%e A260167 G.f. = q^23 + 2*q^47 + 3*q^71 + 3*q^95 + 4*q^119 + 7*q^143 + 7*q^167 + ...
%t A260167 a[ n_] := SeriesCoefficient[ (1/2) x^(-1/2) EllipticTheta[ 2, 0, x^2] QPochhammer[ x^3]^3 QPochhammer[ -x, x]^2, {x, 0, n}];
%o A260167 (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^8 + A)^2 / (eta(x + A)^2 * eta(x^4 + A)), n))};
%Y A260167 Cf. A260158.
%K A260167 nonn
%O A260167 0,2
%A A260167 _Michael Somos_, Nov 09 2015