cp's OEIS Frontend

A192323 Expansion of theta_3(q^3) * theta_3(q^5) in powers of q.

%I A192323 #20 Oct 14 2018 09:17:19
%S A192323 1,0,0,2,0,2,0,0,4,0,0,0,2,0,0,0,0,4,0,0,2,0,0,4,0,0,0,2,0,0,0,0,8,0,
%T A192323 0,0,0,0,0,0,0,0,0,0,0,2,0,4,6,0,0,0,0,4,0,0,0,4,0,0,0,0,0,0,0,0,0,0,
%U A192323 4,0,0,0,4,0,0,2,0,0,0,0,6,0,0,4,0,0,0,0,0,0,0,0,4,4,0,4,0,0,0,0,0,0,0,0,0
%N A192323 Expansion of theta_3(q^3) * theta_3(q^5) in powers of q.
%H A192323 Seiichi Manyama, <a href="/A192323/b192323.txt">Table of n, a(n) for n = 0..10000</a>
%F A192323 Expansion of (eta(q^6) * eta(q^10))^5 / (eta(q^3) * eta(q^5) * eta(q^12) * eta(q^20))^2 in powers of q.
%F A192323 Euler transform of a period 60 sequence.
%F A192323 G.f.: (Sum_{k} x^(3 * k^2)) * (Sum_{k} x^(5 * k^2)).
%F A192323 a(3*n + 1) = a(4*n + 2) = a(5*n + 1) = a(5*n + 4) = 0. a(4*n) = A028956(n).
%F A192323 a(n) = A122855(n) - A140727(n). a(5*n) = A260671(n).
%e A192323 G.f. = 1 + 2*q^3 + 2*q^5 + 4*q^8 + 2*q^12 + 4*q^17 + 2*q^20 + 4*q^23 + 2*q^27 + ...
%t A192323 a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q^3] EllipticTheta[ 3, 0, q^5], {q, 0, n}];
%o A192323 (PARI) {a(n) = if( n<1, n==0, qfrep([3, 0; 0, 5], n)[n]*2)};
%o A192323 (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^6 + A) * eta(x^10 + A))^5 / (eta(x^3 + A) * eta(x^5 + A) * eta(x^12 + A) * eta(x^20 + A))^2, n))};
%Y A192323 Cf. A028956, A122855, A140727, A260671.
%K A192323 nonn
%O A192323 0,4
%A A192323 _Michael Somos_, Aug 01 2011