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

0,3

Links

Seiichi Manyama, Rows n = 0..26, flattened

Example

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;

Prog

(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)

Crossrefs

Cf. A010816, A231599, A304080.

Sequence in context: A214281 A125300 A371741 * A365213 A126717 A124039

Adjacent sequences: A303989 A303990 A303991 * A303993 A303994 A303995

Keyword

sign,tabf

Author

Seiichi Manyama, May 04 2018

Status

approved