A108041 Triangle of numbers {a(n,k), n >= 0, 0<=k<=n} defined by a(0,0)=1, a(n,0)=a(n-1,n-1), a(n,k)=a(n,k-1) + Sum_{i=0..k-1} a(n-1,i).

1, 1, 2, 2, 3, 7, 7, 9, 19, 42, 42, 49, 100, 210, 443, 443, 485, 977, 2005, 4120, 8473, 8473, 8916, 17874, 36240, 73508, 149131, 302615, 302615, 311088, 622619, 1254196, 2526758, 5090784, 10257191, 20667866, 20667866, 20970481, 41949435, 84210401, 169052379

Offset: 0

Author

N. J. A. Sloane, Jun 01 2005

Keywords

• tabl
• nonn

Examples

			1; 1,2; 2,3,7; 7,9,19,42; 42,49,100,210,443; ...
		

Crossrefs

Borders give A108042. Row sums are A108043. Cf. A011971.

Programs

Maple

f := proc(n,k) local i,t1; option remember; if n=0 and k=0 then 1 elif k=0 then f(n-1,n-1) else add(f(n,i),i=0..k-1) +f(n-1,k-1); fi: end;