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A284501 Expansion of Product_{k>=0} (1 - x^(7*k+3)) in powers of x.

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%I A284501 #14 Jan 17 2023 15:00:44
%S A284501 1,0,0,-1,0,0,0,0,0,0,-1,0,0,1,0,0,0,-1,0,0,1,0,0,0,-1,0,0,2,0,0,-1,
%T A284501 -1,0,0,2,0,0,-1,-1,0,0,3,0,0,-2,-1,0,0,3,0,0,-3,-1,0,1,4,0,0,-4,-1,0,
%U A284501 1,4,0,0,-5,-1,0,2,5,0,0,-7,-1,0,3,5,0,0,-8,-1,0,5
%N A284501 Expansion of Product_{k>=0} (1 - x^(7*k+3)) in powers of x.
%H A284501 Seiichi Manyama, <a href="/A284501/b284501.txt">Table of n, a(n) for n = 0..10000</a>
%F A284501 a(n) = -(1/n)*Sum_{k=1..n} A284444(k)*a(n-k), a(0) = 1.
%t A284501 CoefficientList[Series[Product[1 - x^(7k + 3), {k, 0, 100}], {x, 0, 100}], x] (* _Indranil Ghosh_, Mar 28 2017 *)
%o A284501 (PARI) Vec(prod(k=0, 100, 1 - x^(7*k + 3)) + O(x^101)) \\ _Indranil Ghosh_, Mar 28 2017
%Y A284501 Cf. Product_{k>=0} (1 - x^(7*k+m)): A284499 (m=1), A284500 (m=2), this sequence (m=3), A284502 (m=4), A284503 (m=5), A284504 (m=6).
%Y A284501 Cf. A281457.
%K A284501 sign,look
%O A284501 0,28
%A A284501 _Seiichi Manyama_, Mar 28 2017