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%I #12 Jan 17 2023 12:29:00
%S 1,0,-1,0,0,0,0,0,0,-1,0,1,0,0,0,0,-1,0,1,0,0,0,0,-1,0,2,0,-1,0,0,-1,
%T 0,2,0,-1,0,0,-1,0,3,0,-2,0,0,-1,0,3,0,-3,0,1,-1,0,4,0,-4,0,1,-1,0,4,
%U 0,-5,0,2,-1,0,5,0,-7,0,3,-1,0,5,0,-8,0,5,-1,-1
%N Expansion of Product_{k>=0} (1 - x^(7*k+2)) in powers of x.
%H Robert Israel, <a href="/A284500/b284500.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = -(1/n)*Sum_{k=1..n} A284443(k)*a(n-k), a(0) = 1.
%p S:= series(mul(1-x^(7*k+2),k=0..(100-2)/7),x,101):
%p seq(coeff(S,x,i),i=0..100); # _Robert Israel_, Jan 17 2023
%t CoefficientList[Series[Product[1 - x^(7k + 2), {k, 0, 100}], {x, 0, 100}], x] (* _Indranil Ghosh_, Mar 28 2017 *)
%o (PARI) Vec(prod(k=0, 100, 1 - x^(7*k + 2)) + O(x^101)) \\ _Indranil Ghosh_, Mar 28 2017
%Y Cf. Product_{k>=0} (1 - x^(7*k+m)): A284499 (m=1), this sequence (m=2), A284501 (m=3), A284502 (m=4), A284503 (m=5), A284504 (m=6).
%Y Cf. A281458.
%K sign,look
%O 0,26
%A _Seiichi Manyama_, Mar 28 2017
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