A168577 Pascal's triangle, first two columns and diagonal removed.

3, 6, 4, 10, 10, 5, 15, 20, 15, 6, 21, 35, 35, 21, 7, 28, 56, 70, 56, 28, 8, 36, 84, 126, 126, 84, 36, 9, 45, 120, 210, 252, 210, 120, 45, 10, 55, 165, 330, 462, 462, 330, 165, 55, 11, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 78, 286, 715, 1287, 1716, 1716, 1287

Offset

2,1

Comments

Row sums are 3, 10, 25, 56, 119, 246, .. (A000247).

Links

Table of n, a(n) for n=2..63.

Formula

T(n,k)= [x^k] ((x + 1)^n - x^n - n*x - 1), 2<=k<n.

T(n,k) = binomial(n,k).

Example

3;
6, 4;
10, 10, 5;
15, 20, 15, 6;
21, 35, 35, 21, 7;
28, 56, 70, 56, 28, 8;
36, 84, 126, 126, 84, 36, 9;
45, 120, 210, 252, 210, 120, 45, 10;
55, 165, 330, 462, 462, 330, 165, 55, 11;
66, 220, 495, 792, 924, 792, 495, 220, 66, 12;
78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13;

Mathematica

p[x_, n_] = ((x + 1)^n - x^n - n*x - 1)/x^2;
Table[CoefficientList[p[x, n], x], {n, 3, 13}];
Flatten[%]

Crossrefs

Cf. A007318, A104712

Sequence in context: A294671 A275985 A163294 * A122634 A169846 A169854

Adjacent sequences: A168574 A168575 A168576 * A168578 A168579 A168580

Keyword

nonn,easy,tabl

Author

Roger L. Bagula, Nov 30 2009

Status

approved