A303992 Triangular array T(n,k) giving coefficients in expansion of Product_{j=1..n} (1-x^j)^3.
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, 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, -24, -21, 24, 9, 9, -6, -13, 3, 0, 5, 0, -3, 1
Offset: 0
Examples
Irregular triangle starts: n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 ---+----------------------------------------------------------------------- 0 | 1; 1 | 1, -3, 3, -1; 2 | 1, -3, 0, 8, -6, -6, 8, 0, -3, 1; 3 | 1, -3, 0, 5, 3, -6, -13, 9, 15, 0, -15, -9, 13, 6, -3, -5, 0, 3, -1;
Links
- Seiichi Manyama, Rows n = 0..26, flattened
Programs
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PARI
T(n, k) = polcoef(prod(j=1, n, (1-x^j)^3), k); tabf(nn) = for(n=0, nn, for(k=0, 3*n*(n+1)/2, print1(T(n, k), ", ")); print)