A089899 Square array, read by antidiagonals, where the n-th row is the binomial transform of (1+x+x^2)^n, starting with n=0.

1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 8, 7, 1, 1, 5, 13, 18, 11, 1, 1, 6, 19, 35, 36, 16, 1, 1, 7, 26, 59, 83, 66, 22, 1, 1, 8, 34, 91, 160, 179, 113, 29, 1, 1, 9, 43, 132, 276, 392, 358, 183, 37, 1, 1, 10, 53, 183, 441, 752, 886, 673, 283, 46, 1, 1, 11, 64, 245, 666, 1317, 1882, 1874

Offset: 0

Author

Paul D. Hanna, Nov 13 2003

Keywords

• nonn
• tabl

Comments

Main diagonal is A082759, antidiagonal sums give A052921.

Examples

			Row 3 = {1,4,13,35,83,179,...} = BINOMIAL({1,3,6,7,6,3,1}).
Rows begin:
[1,1,1,1,1,1,1,1,..],
[1,2,4,7,11,16,22,29,..],
[1,3,8,18,36,66,113,183,..],
[1,4,13,35,83,179,358,673,..],
[1,5,19,59,160,392,886,1874,..],
[1,6,26,91,276,752,1882,4392,..],
[1,7,34,132,441,1317,3599,9143,..],
[1,8,43,183,666,2157,6371,17446,..],..
		

Crossrefs

Cf. A082759, A052921.

Programs

PARI

T(n,k)=local(t); if(n<0 || k<0,0, t=sum(j=0,k,binomial(k,j)*polcoeff((1+x+x^2)^n+x*O(x^j),j)))