A284317 - OEIS

%I #14 Mar 27 2017 15:29:04

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

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

%U -1,0,3,-8,6,-1,0,5,-10,6,-1,-1,6,-12,7,-1,-1,9,-14

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

%H Robert Israel, <a href="/A284317/b284317.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = -(1/n)*Sum_{k=1..n} A284103(k)*a(n-k), a(0) = 1.

%F G.f. is the QPochhammer symbol (x^4;x^5)_infinity. - _Robert Israel_, Mar 27 2017

%p S:= series(mul(1-x^(5*k+4),k=0..200),x,101):

%p seq(coeff(S,x,j),j=0..100); # _Robert Israel_, Mar 27 2017

%t CoefficientList[Series[Product[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 + 4)) + O(x^101)) \\ _Indranil Ghosh_, Mar 25 2017

%Y Cf. Product_{k>=0} (1 - x^(m*k+m-1)): A081362 (m=2), A284315 (m=3), A284316 (m=4), this sequence (m=5).

%Y Cf. A281243, A284103.

%K sign

%O 0,24

%A _Seiichi Manyama_, Mar 25 2017