A124788 Triangle read by rows: expansion of (1+x*y)/(1-x^2*y^2-x^3*y^2).

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

Offset: 0

Author

Paul Barry, Nov 07 2006

Keywords

• easy
• nonn
• tabl

Comments

Row sums give A000931(n+5). Diagonal sums are A124789.

Examples

			Triangle begins
1,
0, 1,
0, 0, 1,
0, 0, 1, 1,
0, 0, 0, 1, 1,
0, 0, 0, 0, 2, 1,
0, 0, 0, 0, 1, 2, 1,
0, 0, 0, 0, 0, 1, 3, 1,
0, 0, 0, 0, 0, 0, 3, 3, 1,
0, 0, 0, 0, 0, 0, 1, 3, 4, 1,
0, 0, 0, 0, 0, 0, 0, 1, 6, 4, 1
		

Crossrefs

Cf. A124745.

Programs

Maple

A124788 := proc(n,k) binomial(floor(k/2),n-k) ; end: for n from 0 to 20 do for k from 0 to n do printf("%d, ",A124788(n,k)) ; od ; od ; # R. J. Mathar, Feb 10 2007

Formula

Number triangle T(n,k) = binomial(floor(k/2),n-k).

Column k has g.f. x^k*(1+x)^floor(k/2). - Paul Barry, Feb 01 2007

Extensions

More terms from R. J. Mathar, Feb 10 2007