A298485 Triangle read by rows; row 0 is 1; the n-th row for n>0 contains the coefficients in the expansion of (2-x)*(1+x)^(n-1).

1, 2, -1, 2, 1, -1, 2, 3, 0, -1, 2, 5, 3, -1, -1, 2, 7, 8, 2, -2, -1, 2, 9, 15, 10, 0, -3, -1, 2, 11, 24, 25, 10, -3, -4, -1, 2, 13, 35, 49, 35, 7, -7, -5, -1, 2, 15, 48, 84, 84, 42, 0, -12, -6, -1, 2, 17, 63, 132, 168, 126, 42, -12, -18, -7, -1, 2, 19, 80, 195, 300, 294, 168, 30, -30, -25, -8, -1

Offset

0,2

Links

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

Formula

T(n,k) = T(n-1,k-1)+T(n-1,k); T(0,0)=1, T(1,0)=2, T(1,1)=-1.

Example

Triangle begins:
1;
2, -1;
2,  1, -1;
2,  3,  0, -1;
2,  5,  3, -1, -1;
2,  7,  8,  2, -2, -1;
2,  9, 15, 10,  0, -3, -1;
2, 11, 24, 25, 10, -3, -4, -1;
2, 13, 35, 49, 35,  7, -7, -5, -1;
...

Mathematica

T[0, 0] = 1; T[_, 0] = 2; T[1, 1] = -1; T[n_?Positive, k_?Positive] := T[n, k] = T[n - 1, k - 1] + T[n - 1, k]; T[_, _] = 0; Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-François Alcover, Feb 05 2018 *)

Crossrefs

Central column gives A088218.

Cf. A037012.

Sequence in context: A211352 A087187 A029380 * A332997 A298614 A108129

Adjacent sequences: A298482 A298483 A298484 * A298486 A298487 A298488

Keyword

sign,tabl

Author

Seiichi Manyama, Jan 20 2018

Status

approved