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A059674
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Square array a(m,n) = binomial(max(m,n), min(m,n)) (m>=0, n>=0) read by antidiagonals.
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2
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1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 1, 3, 1, 1, 4, 3, 3, 4, 1, 1, 5, 6, 1, 6, 5, 1, 1, 6, 10, 4, 4, 10, 6, 1, 1, 7, 15, 10, 1, 10, 15, 7, 1, 1, 8, 21, 20, 5, 5, 20, 21, 8, 1, 1, 9, 28, 35, 15, 1, 15, 35, 28, 9, 1, 1, 10, 36, 56, 35, 6, 6, 35, 56, 36, 10, 1, 1, 11, 45, 84, 70, 21, 1, 21, 70, 84
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OFFSET
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0,8
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LINKS
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FORMULA
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Square array equals A007318 + transpose(A007318) - I, where I denotes the infinite identity matrix. - Peter Bala, Aug 11 2015
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EXAMPLE
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a(2,4) = binomial(max(2,4), min(2,4)) = binomial(4,2) = 6.
Square begins:
1 1 1 1 1 1 ...
1 1 2 3 4 5 ...
1 2 1 3 6 10...
1 3 3 1 4 10 ...
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MATHEMATICA
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a[m_, n_] := If[m >= n, Binomial[m, n], Binomial[n, m]]; Table[a[m-n, n], {m, 0, 12}, {n, 0, m}] // Flatten (* Jean-François Alcover, Oct 10 2012 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Feb 06 2001
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STATUS
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approved
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