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A284320 Expansion of Product_{k>=0} (1 - x^(5*k+3)) in powers of x.

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%I A284320 #19 Dec 14 2017 02:41:12
%S A284320 1,0,0,-1,0,0,0,0,-1,0,0,1,0,-1,0,0,1,0,-1,0,0,2,0,-1,-1,0,2,0,-1,-1,
%T A284320 0,3,0,-1,-2,0,3,0,-1,-3,0,4,1,-1,-4,0,4,1,-1,-5,0,5,2,-1,-7,0,5,3,-1,
%U A284320 -8,0,6,5,-1,-10,-1,6,6,-1,-12,-1,7,9,-1,-14,-2,7,11
%N A284320 Expansion of Product_{k>=0} (1 - x^(5*k+3)) in powers of x.
%H A284320 G. C. Greubel, <a href="/A284320/b284320.txt">Table of n, a(n) for n = 0..10000</a>
%F A284320 a(n) = -(1/n)*Sum_{k=1..n} A284281(k)*a(n-k), a(0) = 1.
%t A284320 CoefficientList[Series[Product[1 - x^(5k + 3), {k, 0, 100}], {x, 0, 100}], x] (* _Indranil Ghosh_, Mar 25 2017 *) (* or *)
%t A284320 a[0]=1; a[n_]:=a[n]= -(1/n) Sum[ a[n-k] DivisorSum[k, # &, Mod[#,5] == 3 &], {k, n}]; a /@ Range[0, 100] (* _Giovanni Resta_, Mar 25 2017 *)
%o A284320 (PARI) Vec(prod(k=0, 100, 1 - x^(5*k + 3)) + O(x^101)) \\ _Indranil Ghosh_, Mar 25 2017
%Y A284320 Cf. Product_{k>=0} (1 - x^(5*k+m)): A284314 (m=1), A284319 (m=2), this sequence (m=3), A284317 (m=4).
%Y A284320 Cf. A281271, A284281.
%K A284320 sign
%O A284320 0,22
%A A284320 _Seiichi Manyama_, Mar 25 2017