%I #54 Mar 11 2018 05:09:58

%S 1,2,-2,6,-3,-3,8,0,-8,0,20,-5,-5,-5,-5,12,6,-6,-12,-6,6,42,-7,-7,-7,

%T -7,-7,-7,32,0,0,0,-32,0,0,0,54,0,0,-27,0,0,-27,0,0,40,10,-10,10,-10,

%U -40,-10,10,-10,10,110,-11,-11,-11,-11,-11,-11,-11,-11,-11,-11

%N Triangle read by rows T(n,k) giving coefficients in expansion of Product_{j=1..n} (1-x^j)^2 mod x^(n+1)-1.

%H Seiichi Manyama, <a href="/A298983/b298983.txt">Rows n = 0..139, flattened</a>

%F T(n,k) = (n+1) * Sum_{d | gcd(n+1,n+1-k)} d*mu((n+1)/d) for 0 <= k <= n.

%F So T(n,0) = A002618(n+1) and T(n,n) = A055615(n+1).

%e Triangle begins:

%e k 0 1 2 3 4 5 6

%e n

%e 0 1;

%e 1 2, -2;

%e 2 6, -3, -3;

%e 3 8, 0, -8, 0;

%e 4 20, -5, -5, -5, -5;

%e 5 12, 6, -6, -12, -6, 6;

%e 6 42, -7, -7, -7, -7, -7, -7;

%Y Cf. A002618, A055615, A282634, A300628.

%K sign,tabl

%O 0,2

%A _Seiichi Manyama_, Mar 10 2018