cp's OEIS Frontend

A284499 Expansion of Product_{k>=0} (1 - x^(7*k+1)) in powers of x.

%I A284499 #18 Jan 18 2023 02:20:01
%S A284499 1,-1,0,0,0,0,0,0,-1,1,0,0,0,0,0,-1,1,0,0,0,0,0,-1,2,-1,0,0,0,0,-1,2,
%T A284499 -1,0,0,0,0,-1,3,-2,0,0,0,0,-1,3,-3,1,0,0,0,-1,4,-4,1,0,0,0,-1,4,-5,2,
%U A284499 0,0,0,-1,5,-7,3,0,0,0,-1,5,-8,5,-1,0,0,-1,6,-10
%N A284499 Expansion of Product_{k>=0} (1 - x^(7*k+1)) in powers of x.
%H A284499 Robert Israel, <a href="/A284499/b284499.txt">Table of n, a(n) for n = 0..10000</a>
%F A284499 a(n) = -(1/n)*Sum_{k=1..n} A284099(k)*a(n-k), a(0) = 1.
%p A284499 G:= mul(1-x^(7*k+1),k=0..100/7):
%p A284499 S:= series(G,x,101):
%p A284499 seq(coeff(S,x,j),j=0..100); # _Robert Israel_, Mar 29 2017
%t A284499 CoefficientList[Series[Product[1 - x^(7k + 1), {k, 0, 100}], {x, 0, 100}], x] (* _Indranil Ghosh_, Mar 28 2017 *)
%o A284499 (PARI) Vec(prod(k=0, 100, 1 - x^(7*k + 1)) + O(x^101)) \\ _Indranil Ghosh_, Mar 28 2017
%Y A284499 Cf. Product_{k>=0} (1 - x^(7*k+m)): this sequence (m=1), A284500 (m=2), A284501 (m=3), A284502 (m=4), A284503 (m=5), A284504 (m=6).
%Y A284499 Cf. A280457.
%K A284499 sign,look
%O A284499 0,24
%A A284499 _Seiichi Manyama_, Mar 28 2017