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A298983 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.

%I A298983 #54 Mar 11 2018 05:09:58
%S A298983 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 A298983 -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 A298983 -40,-10,10,-10,10,110,-11,-11,-11,-11,-11,-11,-11,-11,-11,-11
%N A298983 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 A298983 Seiichi Manyama, <a href="/A298983/b298983.txt">Rows n = 0..139, flattened</a>
%F A298983 T(n,k) = (n+1) * Sum_{d | gcd(n+1,n+1-k)} d*mu((n+1)/d) for 0 <= k <= n.
%F A298983 So T(n,0) = A002618(n+1) and T(n,n) = A055615(n+1).
%e A298983 Triangle begins:
%e A298983   k   0    1    2    3    4    5    6
%e A298983 n
%e A298983 0     1;
%e A298983 1     2,  -2;
%e A298983 2     6,  -3,  -3;
%e A298983 3     8,   0,  -8,   0;
%e A298983 4    20,  -5,  -5,  -5,  -5;
%e A298983 5    12,   6,  -6, -12,  -6,   6;
%e A298983 6    42,  -7,  -7,  -7,  -7,  -7,  -7;
%Y A298983 Cf. A002618, A055615, A282634, A300628.
%K A298983 sign,tabl
%O A298983 0,2
%A A298983 _Seiichi Manyama_, Mar 10 2018