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A140880
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Triangle read by rows, T(n,k) = Gamma(n+3)/(Gamma(k+1)*Gamma(n-k+1)) for n>=0 and 0<=k<=n.
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0
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2, 6, 6, 12, 24, 12, 20, 60, 60, 20, 30, 120, 180, 120, 30, 42, 210, 420, 420, 210, 42, 56, 336, 840, 1120, 840, 336, 56, 72, 504, 1512, 2520, 2520, 1512, 504, 72, 90, 720, 2520, 5040, 6300, 5040, 2520, 720, 90
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listen;
history;
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OFFSET
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0,1
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LINKS
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EXAMPLE
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Triangle starts:
[0] 2
[1] 6, 6
[2] 12, 24, 12
[3] 20, 60, 60, 20
[4] 30, 120, 180, 120, 30
[5] 42, 210, 420, 420, 210, 42
[6] 56, 336, 840, 1120, 840, 336, 56
[7] 72, 504, 1512, 2520, 2520, 1512, 504, 72
[8] 90, 720, 2520, 5040, 6300, 5040, 2520, 720, 90
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MAPLE
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T := (n, k) -> GAMMA(n+3)/(GAMMA(k+1)*GAMMA(n-k+1)):
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MATHEMATICA
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Flatten[Table[Gamma[n+3]/(Gamma[k+1]Gamma[n-k+1]), {n, 0, 8}, {k, 0, n}]]
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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