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Triangular array T(n,k) giving coefficients in expansion of Product_{j=1..n} (1-x^j)^3.
2

%I #29 Oct 14 2019 04:26:15

%S 1,1,-3,3,-1,1,-3,0,8,-6,-6,8,0,-3,1,1,-3,0,5,3,-6,-13,9,15,0,-15,-9,

%T 13,6,-3,-5,0,3,-1,1,-3,0,5,0,3,-13,-6,9,9,24,-21,-24,-9,3,44,3,-9,

%U -24,-21,24,9,9,-6,-13,3,0,5,0,-3,1

%N Triangular array T(n,k) giving coefficients in expansion of Product_{j=1..n} (1-x^j)^3.

%H Seiichi Manyama, <a href="/A303992/b303992.txt">Rows n = 0..26, flattened</a>

%e Irregular triangle starts:

%e n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

%e ---+-----------------------------------------------------------------------

%e 0 | 1;

%e 1 | 1, -3, 3, -1;

%e 2 | 1, -3, 0, 8, -6, -6, 8, 0, -3, 1;

%e 3 | 1, -3, 0, 5, 3, -6, -13, 9, 15, 0, -15, -9, 13, 6, -3, -5, 0, 3, -1;

%o (PARI) T(n, k) = polcoef(prod(j=1, n, (1-x^j)^3), k);

%o tabf(nn) = for(n=0, nn, for(k=0, 3*n*(n+1)/2, print1(T(n, k), ", ")); print)

%Y Cf. A010816, A231599, A304080.

%K sign,tabf

%O 0,3

%A _Seiichi Manyama_, May 04 2018