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A133101 Expansion of f(x^2, x^3) in powers of x where f(, ) is Ramanujan's general theta function.

%I A133101 #13 Jun 16 2016 10:36:40
%S A133101 1,0,1,1,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,
%T A133101 0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,
%U A133101 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0
%N A133101 Expansion of f(x^2, x^3) in powers of x where f(, ) is Ramanujan's general theta function.
%H A133101 Seiichi Manyama, <a href="/A133101/b133101.txt">Table of n, a(n) for n = 0..10000</a>
%H A133101 <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F A133101 The characteristic function of A057569.
%F A133101 Euler transform of period 10 sequence [ 0, 1, 1, -1, -1, -1, 1, 1, 0, -1, ...].
%F A133101 G.f.: Prod_{k>0} (1 - x^(5*k)) * (1 + x^(5*k - 2)) * (1 + x^(5*k - 3)) = Sum_{k in Z} x^((5*k^2 + k) / 2).
%F A133101 a(n) = abs(A113428(n)).
%e A133101 G.f. = 1 + x^2 + x^3 + x^9 + x^11 + x^21 + x^24 + x^38 + x^42 + x^60 + x^65 + ...
%e A133101 G.f. = q + q^81 + q^121 + q^361 + q^441 + q^841 + q^961 + q^1521 + q^1681 + ...
%t A133101 a[ n_] := SeriesCoefficient[ QPochhammer[ -x^2, x^5] QPochhammer[ -x^3, x^5] QPochhammer[ x^5], {x, 0, n}]; (* _Michael Somos_, Oct 31 2015 *)
%o A133101 (PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1,n, 1 + x^k*[ -1, 0, 1, 1, 0][k%5 + 1], 1 + x * O(x^n)), n))};
%Y A133101 Cf. A057569, A113428.
%K A133101 nonn
%O A133101 0,1
%A A133101 _Michael Somos_, Sep 11 2007