A304080 Triangular array T(n,k) giving coefficients in expansion of Product_{j=1..n} (1-x^j)^2.

1, 1, -2, 1, 1, -2, -1, 4, -1, -2, 1, 1, -2, -1, 2, 3, 0, -6, 0, 3, 2, -1, -2, 1, 1, -2, -1, 2, 1, 4, -4, -4, -2, 0, 10, 0, -2, -4, -4, 4, 1, 2, -1, -2, 1, 1, -2, -1, 2, 1, 2, 0, -2, -6, -2, 3, 6, 5, 2, -3, -12, -3, 2, 5, 6, 3, -2, -6, -2, 0, 2, 1, 2, -1, -2, 1

Offset

0,3

Links

Seiichi Manyama, Rows n = 0..30, 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  19 20
---+-----------------------------------------------------------------------------
0  | 1;
1  | 1, -2,  1;
2  | 1, -2, -1, 4, -1, -2,  1;
3  | 1, -2, -1, 2,  3,  0, -6,  0,  3, 2, -1, -2,  1;
4  | 1, -2, -1, 2,  1,  4, -4, -4, -2, 0, 10,  0, -2, -4, -4, 4, 1, 2, -1, -2, 1;

Prog

(PARI) T(n, k) = polcoef(prod(j=1, n, (1-x^j)^2), k);
tabf(nn) = for(n=0, nn, for(k=0, n*(n+1), print1(T(n, k), ", ")); print)

Crossrefs

Cf. A002107, A231599, A303992.

Sequence in context: A138650 A266685 A272620 * A137843 A130194 A113926

Adjacent sequences: A304077 A304078 A304079 * A304081 A304082 A304083

Keyword

sign,tabf

Author

Seiichi Manyama, May 06 2018

Status

approved