A125231 Triangle read by rows: T(n,k) = ceiling((k+1)/2)*binomial(n,k) (0 <= k <= n).

1, 1, 1, 1, 2, 2, 1, 3, 6, 2, 1, 4, 12, 8, 3, 1, 5, 20, 20, 15, 3, 1, 6, 30, 40, 45, 18, 4, 1, 7, 42, 70, 105, 63, 28, 4, 1, 8, 56, 112, 210, 168, 112, 32, 5, 1, 9, 72, 168, 378, 378, 336, 144, 45, 5, 1, 10, 90, 240, 630, 756, 840, 480, 225, 50, 6, 1, 11, 110, 330, 990, 1386, 1848

Offset: 0

Author

Gary W. Adamson, Nov 24 2006

Keywords

• nonn
• tabl

Comments

Row sums = A045623: (1, 2, 5, 12, 28, 64, 144, 320, ...).

A125230 is another triangle with row sums = A045623.

Examples

			First few rows of the triangle:
  1;
  1,   1;
  1,   2,   2;
  1,   3,   6,   2;
  1,   4,  12,   8,   3;
  1,   5,  20,  20,  15,   3;
  1,   6,  30,  40,  45,  18,   4;
  1,   7,  42,  70, 105,  63,  28,   4;
  ...
		

Crossrefs

Cf. A045623, A125230.

Programs

Maple

T:=(n,k)->ceil((k+1)/2)*binomial(n,k): for n from 0 to 12 do seq(T(n,k),k=0..n) od; # yields sequence in triangular form

Mathematica

Flatten[Table[Ceiling[(k+1)/2]Binomial[n,k],{n,0,20},{k,0,n}]] (* Harvey P. Dale, Aug 31 2015 *)

Extensions

Edited by N. J. A. Sloane, Dec 02 2006