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A065420
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Triangle T(n,k) = binomial(n+2,k+1)*(binomial(n+2,k+1)-1), n >=0, 0 <= k <= n.
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2
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2, 6, 6, 12, 30, 12, 20, 90, 90, 20, 30, 210, 380, 210, 30, 42, 420, 1190, 1190, 420, 42, 56, 756, 3080, 4830, 3080, 756, 56, 72, 1260, 6972, 15750, 15750, 6972, 1260, 72, 90, 1980, 14280, 43890, 63252, 43890, 14280, 1980, 90, 110, 2970, 27060, 108570, 212982
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OFFSET
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0,1
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COMMENTS
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LINKS
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FORMULA
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T(n,0) = (n+1)*(n+2) = A002378(n+1).
T(n,1) = n*(n+1)*(n+2)*(n+3)/4 = A033487(n). (End)
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EXAMPLE
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2; 6,6; 12,30,12; 20,90,90,20; ...
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MAPLE
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T:= (n, k) -> binomial(n+2, k+1)*(binomial(n+2, k+1)-1):
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MATHEMATICA
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#(#-1)&/@Table[Binomial[n+2, k+1], {n, 0, 10}, {k, 0, n}]//Flatten (* Harvey P. Dale, Sep 02 2018 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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Gary W. Adamson, Nov 15 2001
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EXTENSIONS
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STATUS
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approved
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