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%I #10 Sep 08 2022 08:45:41
%S 2,7,7,37,18,37,221,78,78,221,1366,470,210,470,1366,8569,3078,969,969,
%T 3078,8569,54265,20370,6195,2660,6195,20370,54265,346105,134620,42780,
%U 12650,12650,42780,134620,346105,2220076,888057,296361,83655,35100,83655,296361,888057,2220076
%N Triangle read by rows: T(n, k) = binomial(3*n, k-1) + binomial(3*n, n-k).
%C Row sums are: {2, 14, 92, 598, 3882, 25232, 164320, 1072310, 7011398, 45928174, ...}.
%H G. C. Greubel, <a href="/A156003/b156003.txt">Rows n = 1..100 of triangle, flattened</a>
%H B. Brainerd and T. V. Narayana, <a href="http://dx.doi.org/10.1214/aoms/1177704987">A Note on Simple Binomial Sampling Plans</a>, Ann. Math. Statist. Volume 32, Number 3 (1961), 906-908.
%F T(n, k) = binomial(3*n, k-1) + binomial(3*n, n-k).
%e Triangle begins as:
%e 2;
%e 7, 7;
%e 37, 18, 37;
%e 221, 78, 78, 221;
%e 1366, 470, 210, 470, 1366;
%e 8569, 3078, 969, 969, 3078, 8569;
%e 54265, 20370, 6195, 2660, 6195, 20370, 54265;
%e 346105, 134620, 42780, 12650, 12650, 42780, 134620, 346105;
%e 2220076, 888057, 296361, 83655, 35100, 83655, 296361, 888057, 2220076;
%p 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
%t Table[Binomial[3*n, k-1] + Binomial[3*n, n-k], {n,10}, {k,n}]//Flatten
%o (PARI) T(n,k) = my(b=binomial); b(3*n, k-1) + b(3*n, n-k); \\ _G. C. Greubel_, Dec 01 2019
%o (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
%o (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
%o (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
%K nonn,tabl
%O 1,1
%A _Roger L. Bagula_, Feb 01 2009
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