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A357079
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Triangle read by rows. T(n, k) = A356265(n, k) + A357078(n, k) for 0 <= k <= n.
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1
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1, 0, 1, 0, 1, 1, 0, 3, 2, 1, 0, 9, 12, 2, 1, 0, 49, 37, 31, 2, 1, 0, 329, 149, 176, 63, 2, 1, 0, 2561, 794, 853, 702, 127, 2, 1, 0, 22369, 5599, 3836, 5709, 2549, 255, 2, 1, 0, 216225, 47275, 18422, 37609, 33949, 8886, 511, 2, 1, 2291457, 451176, 107535, 218506, 344670, 184653, 29777, 1023, 2, 1
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refs;
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history;
text;
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OFFSET
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0,8
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COMMENTS
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The triangle is the termwise sum of a refinement of the number of irreducible permutations A357078, and A356265, which is a refinement of the number of reducible permutations.
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LINKS
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EXAMPLE
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Triangle T(n, k) starts: [Row sums]
[0] 1; [1]
[1] 0, 1; [1]
[2] 0, 1, 1; [2]
[3] 0, 3, 2, 1; [6]
[4] 0, 9, 12, 2, 1; [24]
[5] 0, 49, 37, 31, 2, 1; [120]
[6] 0, 329, 149, 176, 63, 2, 1; [720]
[7] 0, 2561, 794, 853, 702, 127, 2, 1; [5040]
[8] 0, 22369, 5599, 3836, 5709, 2549, 255, 2, 1; [40320]
[9] 0, 216225, 47275, 18422, 37609, 33949, 8886, 511, 2, 1; [362880]
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PROG
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(SageMath)
return [[0^n] + [T[n][k+1] + A356265_row(n)[k]
for k in range(n)] for n in range(dim)]
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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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