OFFSET
0,6
COMMENTS
Original name was: "Number triangle T(n,k) = if(k<=n, Sum_{j=0..floor(k/2)} binomial(n+j,j), 0)."
LINKS
Robert Israel, Table of n, a(n) for n = 0..10010 (Rows 0..140, flattened)
FORMULA
EXAMPLE
Rows start:
1;
1, 1;
1, 1, 4;
1, 1, 5, 5;
1, 1, 6, 6, 21;
1, 1, 7, 7, 28, 28;
1, 1, 8, 8, 36, 36, 120;
1, 1, 9, 9, 45, 45, 165, 165;
1, 1, 10, 10, 55, 55, 220, 220, 715;
MAPLE
for n from 0 to 20 do seq(binomial(n+floor(k/2)+1, n+1), k=0..n) od; # Robert Israel, May 08 2018
MATHEMATICA
Table[Binomial[n+Floor[k/2]+1, n+1], {n, 0, 15}, {k, 0, n}]//Flatten (* G. C. Greubel, Jul 24 2022 *)
PROG
(Magma) [Binomial(n+1+Floor(k/2), n+1): k in [0..n], n in [0..15]]; // G. C. Greubel, Jul 24 2022
(SageMath) flatten([[binomial(n+(k//2)+1, n+1) for k in (0..n)] for n in (0..15)]) # G. C. Greubel, Jul 24 2022
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Oct 23 2004
EXTENSIONS
Definition simplified by Robert Israel, May 08 2018
STATUS
approved