A125178 Triangle read by rows: T(n,0)=B(n) (the Bell numbers, A000110(n)), T(n,k)=0 for k < 0 or k > n, T(n,k) = T(n-1,k) + T(n-1,k-1) for n >= 1, 0 <= k <= n.

1, 1, 1, 2, 2, 1, 5, 4, 3, 1, 15, 9, 7, 4, 1, 52, 24, 16, 11, 5, 1, 203, 76, 40, 27, 16, 6, 1, 877, 279, 116, 67, 43, 22, 7, 1, 4140, 1156, 395, 183, 110, 65, 29, 8, 1, 21147, 5296, 1551, 578, 293, 175, 94, 37, 9, 1, 115975, 26443, 6847, 2129, 871, 468, 269, 131, 46, 10, 1

Offset: 0

Author

Gary W. Adamson, Nov 22 2006

Keywords

• nonn
• tabl

Comments

Row sums = 1, 2, 5, 13, 36, 109, 369, ...

Columns 0,1 and 2 yield A000110, A005001 and A029761, respectively.

Examples

			First few rows of the triangle:
    1;
    1,  1;
    2,  2,  1;
    5,  4,  3,  1;
   15,  9,  7,  4,  1;
   52, 24, 16, 11,  5, 1;
  203, 76, 40, 27, 16, 6, 1;
  ...
(4,3) = 16 = 7 + 9 = (3,3) + (3,2).
		

Crossrefs

Cf. A000110, A005001, A029761.

Programs

Maple

with(combinat): T:=proc(n,k) if k=0 then bell(n) elif k<0 or k>n then 0 else T(n-1,k)+T(n-1,k-1) fi end: for n from 0 to 11 do seq(T(n,k),k=0..n) od; # yields sequence in triangular form

Extensions

Edited by N. J. A. Sloane, Nov 29 2006