OFFSET
0,5
COMMENTS
For k <= 6, the triangle coincides with triangle A213745.
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
FORMULA
EXAMPLE
Triangle begins
n/k | 0 1 2 3 4 5 6 7 8
----+---------------------------------------------------
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 56 126 252 462
7 | 1 7 28 84 210 462 924 1716
8 | 1 8 36 120 330 792 1716 3432 6427
MATHEMATICA
Table[Sum[(-1)^r*Binomial[n, r]*Binomial[n - 8*r + k - 1, n - 1], {r, 0, Floor[k/8]}], {n, 0, 10}, {k, 0, n}] // Flatten (* G. C. Greubel, Nov 25 2017 *)
PROG
(PARI) for(n=0, 10, for(k=0, n, print1(if(n==0 && k==0, 1, sum(r=0, floor(k/8), (-1)^r*binomial(n, r)*binomial(n-8*r + k-1, n-1))), ", "))) \\ G. C. Greubel, Nov 25 2017
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Vladimir Shevelev and Peter J. C. Moses, Jun 20 2012
STATUS
approved