A284502 - OEIS

%I #15 Jan 18 2023 02:20:14

%S 1,0,0,0,-1,0,0,0,0,0,0,-1,0,0,0,1,0,0,-1,0,0,0,1,0,0,-1,0,0,0,2,0,0,

%T -1,-1,0,0,2,0,0,-1,-1,0,0,3,0,0,-1,-2,0,0,3,0,0,-1,-3,0,0,4,1,0,-1,

%U -4,0,0,4,1,0,-1,-5,0,0,5,2,0,-1,-7,0,0,5,3,0,-1,-8

%N Expansion of Product_{k>=0} (1 - x^(7*k+4)) in powers of x.

%H Seiichi Manyama, <a href="/A284502/b284502.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = -(1/n) * Sum_{k=1..n} A284445(k) * a(n-k), a(0) = 1.

%t CoefficientList[Series[Product[1 - x^(7k + 4), {k, 0, 100}], {x, 0, 100}], x] (* _Indranil Ghosh_, Mar 28 2017 *)

%o (PARI) Vec(prod(k=0, 100, 1 - x^(7*k + 4)) + O(x^101)) \\ _Indranil Ghosh_, Mar 28 2017

%Y Cf. Product_{k>=0} (1 - x^(7*k+m)): A284499 (m=1), A284500 (m=2), A284501 (m=3), this sequence (m=4), A284503 (m=5), A284504 (m=6).

%Y Cf. A281456.

%K sign,look

%O 0,30

%A _Seiichi Manyama_, Mar 28 2017