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.

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, -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, -40, -10, 10, -10, 10, 110, -11, -11, -11, -11, -11, -11, -11, -11, -11, -11

Offset

0,2

Links

Seiichi Manyama, Rows n = 0..139, flattened

Formula

T(n,k) = (n+1) * Sum_{d | gcd(n+1,n+1-k)} d*mu((n+1)/d) for 0 <= k <= n.

So T(n,0) = A002618(n+1) and T(n,n) = A055615(n+1).

Example

Triangle begins:
  k   0    1    2    3    4    5    6
n
0     1;
1     2,  -2;
2     6,  -3,  -3;
3     8,   0,  -8,   0;
4    20,  -5,  -5,  -5,  -5;
5    12,   6,  -6, -12,  -6,   6;
6    42,  -7,  -7,  -7,  -7,  -7,  -7;

Crossrefs

Cf. A002618, A055615, A282634, A300628.

Sequence in context: A306464 A338449 A163890 * A128623 A182701 A277011

Adjacent sequences: A298980 A298981 A298982 * A298984 A298985 A298986

Keyword

sign,tabl

Author

Seiichi Manyama, Mar 10 2018

Status

approved