A057884 A square array based on tetrahedral numbers (A000292) with each term being the sum of 2 consecutive terms in the previous row.

1, 0, 1, 4, 1, 1, 0, 4, 2, 1, 10, 4, 5, 3, 1, 0, 10, 8, 7, 4, 1, 20, 10, 14, 13, 10, 5, 1, 0, 20, 20, 22, 20, 14, 6, 1, 35, 20, 30, 34, 35, 30, 19, 7, 1, 0, 35, 40, 50, 56, 55, 44, 25, 8, 1, 56, 35, 55, 70, 84, 91, 85, 63, 32, 9, 1, 0, 56, 70, 95, 120, 140, 146, 129, 88, 40, 10, 1

Offset: 0

Author

Henry Bottomley, Nov 20 2000

Keywords

• easy
• nonn
• tabl

Examples

			Rows are (1,0,4,0,10,0,20,...), (1,1,4,4,10,10,20,...), (1,2,5,8,14,20,30,...), (1,3,7,13,22,34,50,...), (1,4,10,20,35,56,84,...) etc.
		

Crossrefs

Rows are A000292 with zeros, A058187 (A000292 with terms duplicated), A006918, A002623, A000292, A000330, A005900, A001845, A008412.

Formula

T(n, k)=T(n-1, k-1)+T(n, k-1) with T(0, k)=1, T(4, 1)=4, T(0, 2n)=T(4, n) and T(0, 2n+1)=0. Coefficient of x^n in expansion of (1+x)^k/(1-x^2)^4.