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A226031
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Number A(n,k) of unimodal functions f:[n]->[k*n]; square array A(n,k), n>=0, k>=0, read by antidiagonals.
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3
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1, 1, 0, 1, 1, 0, 1, 2, 4, 0, 1, 3, 16, 22, 0, 1, 4, 36, 161, 130, 0, 1, 5, 64, 525, 1716, 791, 0, 1, 6, 100, 1222, 8086, 18832, 4900, 0, 1, 7, 144, 2360, 24616, 128248, 210574, 30738, 0, 1, 8, 196, 4047, 58730, 510664, 2072862, 2385644, 194634, 0
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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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A(n,k) = Sum_{j=0..k*n-1} C(n+2*j-1,2*j), A(0,k) = 1.
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EXAMPLE
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Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 4, 16, 36, 64, 100, ...
0, 22, 161, 525, 1222, 2360, ...
0, 130, 1716, 8086, 24616, 58730, ...
0, 791, 18832, 128248, 510664, 1505205, ...
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MAPLE
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A:= (n, k)-> `if`(n=0, 1, add(binomial(n+2*j-1, 2*j), j=0..k*n-1)):
seq(seq(A(n, d-n), n=0..d), d=0..10);
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MATHEMATICA
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A[n_, k_] := If[n==0, 1, Sum[Binomial[n + 2j - 1, 2j], {j, 0, k n - 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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