A191532 Triangle T(n,k) read by rows: T(n,n) = 2n+1, T(n,k)=k for k

1, 0, 3, 0, 1, 5, 0, 1, 2, 7, 0, 1, 2, 3, 9, 0, 1, 2, 3, 4, 11, 0, 1, 2, 3, 4, 5, 13, 0, 1, 2, 3, 4, 5, 6, 15, 0, 1, 2, 3, 4, 5, 6, 7, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 23, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 27

Offset: 0

Author

Paul Curtz, Jun 05 2011

Keywords

• nonn
• easy
• tabl

Comments

We can build products of linear polynomials with these T(n,k) defining the absolute terms:

1+n = A000027(1+n) =2, 3, 4, 5, 6, 7,

n*(3+n)/2 = A000096(1+n) =2, 5, 9, 14, 20, 27,

n*(1+n)*(5+n)/6 = A005581(2+n) =2, 7, 16, 30, 50, 77,

n*(1+n)*(2+n)*(7+n)/24 = A005582(1+n) =2, 9, 25, 55, 105, 182,

n*(1+n)*(2+n)*(3+n)*(9+n)/120 = A005583(n) =2, 11, 36, 91, 196, 378,

n*(1+n)*(2+n)*(3+n)*(4+n)*(11+n)/720 = A005584(n)=2, 13, 49, 140, 336, 714,

Examples

			1;
0,3;
0,1,5;
0,1,2,7;
0,1,2,3,9;
0,1,2,3,4,11;
		

Crossrefs

Cf. A191302.

Formula

T(n,k) = A002262(n-1,k).

sum_{k=0..n} T(n,k) = A000217(1+n).