A284312 - OEIS

%I #17 Oct 09 2017 09:37:56

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

%T 1,5,-7,2,5,-8,4,5,-10,5,5,-12,8,5,-14,10,4,-16,14,3,-19,17,1,-20,22,

%U -1,-23,26,-4,-25,33,-8,-27,38,-13,-28,46,-19,-30,53,-26,-29

%N Expansion of Product_{k>=0} (1 - x^(3*k+1)) in powers of x.

%H Seiichi Manyama, <a href="/A284312/b284312.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = -(1/n)*Sum_{k=1..n} A078181(k)*a(n-k), a(0) = 1.

%t CoefficientList[Series[Product[1 - x^(3k + 1), {k, 0, 100}], {x, 0, 100}], x] (* _Indranil Ghosh_, Mar 25 2017 *)

%o (PARI) Vec(prod(k=0, 100, 1 - x^(3*k + 1)) + O(x^101)) \\ _Indranil Ghosh_, Mar 25 2017

%Y Cf. Product_{k>=0} (1 - x^(m*k+1)): A081362 (m=2), this sequence (m=3), A284313 (m=4), A284314 (m=5).

%Y Cf. A078181, A261612.

%K sign

%O 0,12

%A _Seiichi Manyama_, Mar 24 2017