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A259097
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Triangle read by rows: T(n,r) = binomial(n,r)*binomial(2*n-3*r-4,n-2*r-2)/(n-r-1), n >= 2, r = 0..floor(n/2)-1.
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1
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1, 1, 2, 2, 5, 5, 14, 15, 5, 42, 49, 21, 132, 168, 84, 14, 429, 594, 336, 84, 1430, 2145, 1350, 420, 42, 4862, 7865, 5445, 1980, 330, 16796, 29172, 22022, 9075, 1980, 132, 58786, 109174, 89232, 40898, 10725, 1287, 208012, 411502, 361998, 182182, 55055, 9009, 429, 742900, 1560090, 1469650, 804440, 273273, 55055, 5005
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OFFSET
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2,3
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LINKS
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EXAMPLE
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Triangle begins:
1;
1;
2, 2;
5, 5;
14, 15, 5;
42, 49, 21;
132, 168, 84, 14;
429, 594, 336, 84;
1430, 2145, 1350, 420, 42;
4862, 7865, 5445, 1980, 330;
16796, 29172, 22022, 9075, 1980, 132;
58786, 109174, 89232, 40898, 10725, 1287;
208012, 411502, 361998, 182182, 55055, 9009, 429;
742900, 1560090, 1469650, 804440, 273273, 55055, 5005;
2674440, 5943200, 5969040, 3527160, 1324960, 312312, 40040, 1430;
...
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MAPLE
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T:=(n, r) -> binomial(n, r)*binomial(2*n-3*r-4, n-2*r-2)/(n-r-1);
v:=n->[seq(T(n, r), r=0..floor(n/2)-1)];
for n from 2 to 16 do lprint(v(n)); od:
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MATHEMATICA
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Flatten[Table[Binomial[n, r] Binomial[2n-3r-4, n-2r-2]/(n-r-1), {n, 2, 16}, {r, 0, Floor[(n/2)]-1}]] (* Indranil Ghosh, Feb 20 2017 *)
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PROG
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(Magma) /* As triangle: */ [[Binomial(n, k)*Binomial(2*n-3*k-4, n-2*k-2)/(n-k-1): k in [0..Floor(n/2)-1]]: n in [2..15]]; // Vincenzo Librandi, Jun 22 2015
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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