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A367267
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Triangle read by rows. T(n, k) = binomial(n, k) * binomial(n - 1, k - 1).
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3
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1, 0, 1, 0, 2, 1, 0, 3, 6, 1, 0, 4, 18, 12, 1, 0, 5, 40, 60, 20, 1, 0, 6, 75, 200, 150, 30, 1, 0, 7, 126, 525, 700, 315, 42, 1, 0, 8, 196, 1176, 2450, 1960, 588, 56, 1, 0, 9, 288, 2352, 7056, 8820, 4704, 1008, 72, 1, 0, 10, 405, 4320, 17640, 31752, 26460, 10080, 1620, 90, 1
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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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For k >= 2: T(n, k) = (n / k) * binomial(n-1, k-1)^2.
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EXAMPLE
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Triangle T(n, k) starts:
[0] 1;
[1] 0, 1;
[2] 0, 2, 1;
[3] 0, 3, 6, 1;
[4] 0, 4, 18, 12, 1;
[5] 0, 5, 40, 60, 20, 1;
[6] 0, 6, 75, 200, 150, 30, 1;
[7] 0, 7, 126, 525, 700, 315, 42, 1;
[8] 0, 8, 196, 1176, 2450, 1960, 588, 56, 1;
[9] 0, 9, 288, 2352, 7056, 8820, 4704, 1008, 72, 1;
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MAPLE
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T := (n, k) -> binomial(n, k) * binomial(n - 1, k - 1):
for n from 0 to 6 do seq(T(n, k), k = 0..n) od;
# Or:
T := (n, k) -> if k=0 then k^n elif k=1 then n else (n/k)*binomial(n-1, k-1)^2 fi:
seq(seq(T(n, k), k = 0..n), n = 0..9);
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MATHEMATICA
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A367267[n_, k_]:=Binomial[n, k]Binomial[n-1, k-1];
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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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