cp's OEIS Frontend

A329958 Expansion of q^(-13/24) * eta(q^2)^3 * eta(q^3) * eta(q^6) / eta(q)^2 in powers of q.

%I A329958 #3 Nov 26 2019 15:49:09
%S A329958 1,2,2,3,3,4,4,3,5,3,6,7,4,5,4,8,6,5,7,6,7,8,7,5,8,10,9,4,7,7,9,11,8,
%T A329958 10,5,10,12,7,10,8,10,12,4,10,8,13,15,10,9,5,15,9,12,11,10,12,10,11,
%U A329958 11,12,15,12,6,14,8,11,17,13,12,9,16,17,8,15,10,14
%N A329958 Expansion of q^(-13/24) * eta(q^2)^3 * eta(q^3) * eta(q^6) / eta(q)^2 in powers of q.
%F A329958 Euler transform of period 6 sequence [2, -1, 1, -1, 2, -3, ...].
%F A329958 G.f.: Product_{k>=1} (1 + x^k)^2 * (1 - x^(2*k)) * (1 - x^(3*k)) * (1 - x^(6*k)).
%F A329958 Convolution of A033762 and A080995. Convolution of A010054 and A121444.
%F A329958 G.f. is a period 1 Fourier series which satisfies f(-1 / (144 t)) = (3/2)^(1/2) (t/i)^2 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A329955.
%e A329958 G.f. = 1 + 2*x + 2*x^2 + 3*x^3 + 3*x^4 + 4*x^5 + 4*x^6 + 3*x^7 + 5*x^8 + ...
%e A329958 G.f. = q^13 + 2*q^37 + 2*q^61 + 3*q^85 + 3*q^109 + 4*q^133 + 4*q^157 + ...
%t A329958 a[ n_] := SeriesCoefficient[ QPochhammer[ x^2]^3 QPochhammer[ x^3] QPochhammer[ x^6] / QPochhammer[ x]^2, {x, 0, n}];
%o A329958 (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^3 * eta(x^3 + A) * eta(x^6 + A) / eta(x + A)^2, n))};
%Y A329958 Cf. A010054, A033762, A080995, A121444, A329955.
%K A329958 nonn
%O A329958 0,2
%A A329958 _Michael Somos_, Nov 26 2019