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 A284321 Expansion of Product_{k>=0} (1 - x^(5*k+1))*(1 - x^(5*k+4)) in powers of x. 2

%I

%S 1,-1,0,0,-1,1,-1,1,0,-1,2,-2,1,1,-2,3,-3,2,0,-3,5,-5,3,1,-5,7,-7,4,1,

%T -7,11,-11,6,2,-10,15,-15,9,2,-14,22,-22,12,4,-20,30,-29,17,4,-27,42,

%U -41,23,7,-37,55,-54,31,8,-49,76,-74,41,12,-66,99,-96,55,14

%N Expansion of Product_{k>=0} (1 - x^(5*k+1))*(1 - x^(5*k+4)) in powers of x.

%H Seiichi Manyama, <a href="/A284321/b284321.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = -(1/n)*Sum_{k=1..n} A284150(k)*a(n-k), a(0) = 1.

%t CoefficientList[Series[Product[(1 - x^(5k + 1)) ( 1 - x^(5k + 4)), {k, 0, 100}], {x, 0, 100}],x] (* _Indranil Ghosh_, Mar 25 2017 *)

%o (PARI) Vec(prod(k=0, 100, (1 - x^(5*k + 1)) * (1 - x^(5*k + 4))) + O(x^101)) \\ _Indranil Ghosh_, Mar 25 2017

%Y Cf. A003114, A284150, A284322, A284314, A284317.

%Y Cf. Product_{k>=0} (1 - x^(m*k+1))*(1 - x^(m*k+m-1)): A137569 (m=3), A081362 (m=4), this sequence (m=5), A109389 (m=6).

%K sign

%O 0,11

%A _Seiichi Manyama_, Mar 25 2017

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Last modified September 16 12:39 EDT 2019. Contains 327110 sequences. (Running on oeis4.)