OFFSET
1,1
COMMENTS
Row sums are: {2, 14, 92, 598, 3882, 25232, 164320, 1072310, 7011398, 45928174, ...}.
LINKS
G. C. Greubel, Rows n = 1..100 of triangle, flattened
B. Brainerd and T. V. Narayana, A Note on Simple Binomial Sampling Plans, Ann. Math. Statist. Volume 32, Number 3 (1961), 906-908.
FORMULA
T(n, k) = binomial(3*n, k-1) + binomial(3*n, n-k).
EXAMPLE
Triangle begins as:
2;
7, 7;
37, 18, 37;
221, 78, 78, 221;
1366, 470, 210, 470, 1366;
8569, 3078, 969, 969, 3078, 8569;
54265, 20370, 6195, 2660, 6195, 20370, 54265;
346105, 134620, 42780, 12650, 12650, 42780, 134620, 346105;
2220076, 888057, 296361, 83655, 35100, 83655, 296361, 888057, 2220076;
MAPLE
b:=binomial; seq(seq( b(3*n, k-1) + b(3*n, n-k), k=1..n), n=1..10); # G. C. Greubel, Dec 01 2019
MATHEMATICA
Table[Binomial[3*n, k-1] + Binomial[3*n, n-k], {n, 10}, {k, n}]//Flatten
PROG
(PARI) T(n, k) = my(b=binomial); b(3*n, k-1) + b(3*n, n-k); \\ G. C. Greubel, Dec 01 2019
(Magma) B:=Binomial; [B(3*n, k-1) + B(3*n, n-k): k in [1..n], n in [1..10]]; // G. C. Greubel, Dec 01 2019
(Sage) b=binomial; [[b(3*n, k-1) + b(3*n, n-k) for k in (1..n)] for n in (1..10)] # G. C. Greubel, Dec 01 2019
(GAP) B:=Binomial;; Flat(List([1..10], n-> List([1..n], k-> B(3*n, k-1) + B(3*n, n-k) ))); # G. C. Greubel, Dec 01 2019
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Feb 01 2009
STATUS
approved