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A182930
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Triangle read by rows: Number of set partitions of {1,2,..,n} such that |k| is a block and no block |m| with m < k exists, (1 <= n, 1 <= k <= n).
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3
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1, 1, 0, 2, 1, 1, 5, 3, 2, 1, 15, 10, 7, 5, 4, 52, 37, 27, 20, 15, 11, 203, 151, 114, 87, 67, 52, 41, 877, 674, 523, 409, 322, 255, 203, 162, 4140, 3263, 2589, 2066, 1657, 1335, 1080, 877, 715, 21147, 17007, 13744, 11155, 9089, 7432, 6097, 5017, 4140, 3425
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OFFSET
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1,4
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COMMENTS
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LINKS
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FORMULA
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Recursion: The value of T(n,k) is, if n < 0 or k < 0 or k > n undefined, else if n = 1 then 1 else if k = n then T(n-1,1) - T(n-1,n-1); in all other cases T(n,k) = T(n,k+1) + T(n-1,k).
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EXAMPLE
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T(4,2) = card({2|134, 2|3|14, 2|4|13}) = 3.
[1] 1,
[2] 1, 0,
[3] 2, 1, 1,
[4] 5, 3, 2, 1,
[5] 15, 10, 7, 5, 4,
[6] 52, 37, 27, 20, 15, 11,
[-1-] [-2-] [-3-] [-4-] [-5-] [-6-]
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MAPLE
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T := proc(n, k) option remember; if n = 1 then 1 elif n = k then T(n-1, 1) - T(n-1, n-1) else T(n-1, k) + T(n, k+1) fi end:
A182930 := (n, k) -> T(n, k); seq(print(seq(A182930(n, k), k=1..n)), n=1..6);
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MATHEMATICA
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T[n_, k_] := T[n, k] = Which[n == 1, 1, n == k, T[n-1, 1] - T[n-1, n-1], True, T[n-1, k] + T[n, 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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