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

1,1

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.

Links

Table of n, a(n) for n=1..71.

Example

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, ...

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

Crossrefs

Sequence in context: A182309 A043263 A321326 * A194998 A215190 A214943

Adjacent sequences: A118975 A118976 A118977 * A118979 A118980 A118981

Keyword

nonn,tabl

Author

Gary W. Adamson, May 07 2006

Extensions

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

Status

approved