A118978 Array read by antidiagonals: the n-th row contains the binomial transform of row n-1 of A014410.

2, 3, 2, 4, 6, 2, 5, 10, 9, 2, 6, 15, 20, 12, 2, 7, 21, 35, 34, 15, 2, 8, 28, 56, 70, 52, 18, 2, 9, 36, 84, 126, 125, 74, 21, 2, 10, 45, 120, 210, 252, 205, 100, 24, 2, 11, 55, 165, 330, 462, 461, 315, 130, 27, 2, 12, 66, 220, 495, 792, 924, 786, 460, 164, 30, 2, 13, 78, 286, 715, 1287

Offset: 1

Author

Gary W. Adamson, May 07 2006

Keywords

• nonn
• tabl

Comments

Each row of A014410 is extended by adding an infinite sequence of zeros,

and the binomial transform of this extended row (assuming the first term has index 0) is placed into the array here.

Examples

			First few rows of the array:
  2,  2,  2,  2,   2, ... (binomial transform of 2,0,0,0,0,...)
  3,  6,  9, 12,  15, ... (binomial transform of 3,3,0,0,0,...)
  4, 10, 20, 34,  52, ... (binomial transform of 4,6,4,0,0,...)
  5, 15, 35, 70, 125, ...
		

Programs

Maple

read("transforms") ; A014410 := proc(n,m) if m <= n-1 and m >= 1 then binomial(n,m) ; else 0 ; end if; end proc:
A118978 := proc(n,m) L := [seq(A014410(n+1,k),k=1..m+1) ] ; BINOMIAL(L) ; op(m+1,%) ; end proc:
for d from 1 to 20 do for m from 0 to d-1 do printf("%d,", A118978(d-m,m)) ; end do: printf("\n") ; end do; # R. J. Mathar, Jun 15 2010

Extensions

Edited and extended by R. J. Mathar, Jun 15 2010