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A193636
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Triangle: T(n,k) = C(3n-2k,k), 0 <= k <= n.
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2
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1, 1, 1, 1, 4, 1, 1, 7, 10, 1, 1, 10, 28, 20, 1, 1, 13, 55, 84, 35, 1, 1, 16, 91, 220, 210, 56, 1, 1, 19, 136, 455, 715, 462, 84, 1, 1, 22, 190, 816, 1820, 2002, 924, 120, 1, 1, 25, 253, 1330, 3876, 6188, 5005, 1716, 165, 1, 1, 28, 325, 2024, 7315, 15504, 18564
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OFFSET
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0,5
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LINKS
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FORMULA
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T(n,k) = C(3n-2k,k), 0 <= k <= n.
G.f. as triangle: (1-x*y)^2/(1 - x - 3*x*y + 3*x^2*y^2 - x^3*y^3). - Robert Israel, Nov 06 2018
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EXAMPLE
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First 5 rows:
1;
1, 1;
1, 4, 1;
1, 7, 10, 1;
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MAPLE
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seq(seq(binomial(3*n-2*k, k), k=0..n), n=0..10); # Robert Israel, Nov 06 2018
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MATHEMATICA
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p[n_, k_] := Binomial[3 n - 2 k, k];
Table[p[n, k], {n, 0, 9}, {k, 0, n}] (* A193636 *)
Flatten[%]
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PROG
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(Magma) /* As triangle */[[Binomial(3*n-2*k, k): k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Nov 07 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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