OFFSET
0,7
COMMENTS
A dual to Pascal's triangle. Row n has 2n+1 entries.
LINKS
Ph. Leroux, A simple symmetry generating operads related to rooted planar m-ary trees and polygonal numbers, arXiv:math/0512437 [math.CO], 2005.
Ph. Leroux, A simple symmetry generating operads related to rooted planar m-ary trees and polygonal numbers, J. Integer Seqs., 10 (2007), #07.4.7.
FORMULA
T(n,k) = A070914(n-|n-k|-1,|n-k|+1) if 3<=k<=2n-3 . - R. J. Mathar, Feb 08 2008
EXAMPLE
.............1
...........1.0.1
.........1.0.2.0.1
.......1.0.3.5.3.0.1
....1.0.4.12.14.12.4.0.1
.1.0.5.22.55.42.55.22.5.0.1
MAPLE
A070914 := proc(n, k) binomial(n*(k+1), n)/(n*k+1) ; end proc:
A113206 := proc(n, k) if k = 2 or k = 2*n-2 then 0 ; else A070914(n-abs(n-k)-1, abs(n-k)+1) ; fi ; end proc:
for n from 0 to 10 do for k from 1 to 2*n-1 do printf("%d ", A113206(n, k)) ; od: od: # R. J. Mathar, Feb 08 2008
MATHEMATICA
A070914[n_, k_] := Binomial[n*(k + 1), n]/(n*k + 1);
Table[A113206[n, k], {n, 0, 10}, {k, 1, 2*n - 1}] // Flatten (* Jean-François Alcover, Nov 28 2017, after R. J. Mathar *)
CROSSREFS
KEYWORD
nonn,tabf,easy
AUTHOR
N. J. A. Sloane, Jan 07 2006
STATUS
approved