OFFSET
0,4
COMMENTS
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle, flattened
FORMULA
T(n,k) = binomial( (n-k)*(n+k+1)/2, n-k). - G. C. Greubel, Feb 19 2022
EXAMPLE
Triangle begins:
1;
1, 1;
3, 2, 1;
20, 10, 3, 1;
210, 84, 21, 4, 1;
3003, 1001, 220, 36, 5, 1;
54264, 15504, 3060, 455, 55, 6, 1;
1184040, 296010, 53130, 7315, 816, 78, 7, 1; ...
MATHEMATICA
T[n_, k_]:= Binomial[(n-k)*(n+k+1)/2, n-k];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Feb 19 2022 *)
PROG
(PARI) T(n, k)=binomial(n*(n-1)/2-k*(k-1)/2+n-k, n-k)
(Magma) [Binomial(Floor((n-k)*(n+k+1)/2), n-k): k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 19 2022
(Sage) flatten([[binomial( (n-k)*(n+k+1)/2, n-k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 19 2022
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Jun 04 2005
STATUS
approved