A127718 A007318 * A002260 as infinite lower triangular matrices; A002260 = [1; 1,2; 1,2,3; ...].

1, 2, 2, 4, 6, 3, 8, 14, 12, 4, 16, 30, 33, 20, 5, 32, 62, 78, 64, 30, 6, 64, 126, 171, 168, 110, 42, 7, 128, 254, 360, 396, 320, 174, 56, 8, 256, 510, 741, 876, 815, 558, 259, 72, 9, 512, 1022, 1506, 1864, 1910, 1536, 910, 368, 90, 10, 1024, 2046, 3039, 3872, 4240

Offset: 1

Author

Gary W. Adamson, Jan 25 2007

Keywords

• nonn
• tabl
• easy

Comments

Binomial transform of A002260.

Row sums = A084851: (1, 4, 13, 38, 104, 272, ...) A002260 * A007318 = A127717.

Examples

			First few rows of the triangle:
   1;
   2,   2;
   4,   6,   3;
   8,  14,  12,   4;
  16,  30,  33,  20,   5;
  32,  62,  78,  64,  30,  6;
  64, 126, 171, 168, 110, 42, 7;
  ...
		

Crossrefs

Cf. A002260, A007318, A084851, A127717.

Programs

Maple

A007318 := proc(n,k) binomial(n,k) ; end: A002260 := proc(n,k) if k <= n then k; else 0 ; fi ; end: A127718 := proc(n,k) add( A007318(n-1,i-1)*A002260(i,k),i=1..n) ; end: for n from 1 to 15 do for k from 1 to n do printf("%d,",A127718(n,k)) ; od: od: # R. J. Mathar, Oct 02 2007

Formula

T(n,k) = Sum_{i=1..n} A007318(n-1,i-1)*A002260(i,k). - R. J. Mathar, Oct 02 2007

Extensions

More terms from R. J. Mathar, Oct 02 2007