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 A156003 Triangle read by rows: T(n, k) = binomial(3*n, k-1) + binomial(3*n, n-k). 1
 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 (list; table; graph; refs; listen; history; text; internal format)
 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 Sequence in context: A090521 A090523 A164314 * A306417 A011416 A086658 Adjacent sequences: A156000 A156001 A156002 * A156004 A156005 A156006 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Feb 01 2009 STATUS approved

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Last modified August 7 16:50 EDT 2024. Contains 375017 sequences. (Running on oeis4.)