OFFSET
0,5
COMMENTS
For k<=4, the triangle coincides with triangle A213743.
LINKS
Peter J. C. Moses, Rows n = 0..50 of triangle, flattened
FORMULA
C^(5)(n,k)=sum{r=0,...,floor(k/6)}(-1)^r*C(n,r)*C(n-6*r+k-1, n-1)
EXAMPLE
Triangle begins
n/k.|..0.....1.....2.....3.....4.....5.....6.....7
==================================================
.0..|..1
.1..|..1.....1
.2..|..1.....2.....3
.3..|..1.....3.....6....10
.4..|..1.....4....10....20....35
.5..|..1.....5....15....35....70....126
.6..|..1.....6....21....56...126....252...456
.7..|..1.....7....28....84...210....462...917....1667
MATHEMATICA
Flatten[Table[Sum[(-1)^r Binomial[n, r] Binomial[n-# r+k-1, n-1], {r, 0, Floor[k/#]}], {n, 0, 15}, {k, 0, n}]/.{0}->{1}]&[6] (* Peter J. C. Moses, Apr 16 2013 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Vladimir Shevelev and Peter J. C. Moses, Jun 19 2012
STATUS
approved