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A366138
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Triangle read by rows. T(n, k) = A000326(n - k + 1) * T(n, k - 1) + T(n - 1, k) for 0 < k < n. T(n, 0) = 1 and T(n, n) = T(n, n - 1) if n > 0.
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1
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1, 1, 1, 1, 6, 6, 1, 18, 96, 96, 1, 40, 576, 2976, 2976, 1, 75, 2226, 29688, 151416, 151416, 1, 126, 6636, 175680, 2259576, 11449296, 11449296, 1, 196, 16632, 757800, 18931176, 238623408, 1204566336, 1204566336
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OFFSET
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0,5
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COMMENTS
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This a weighted generalized Catalan triangle (A365673) with the pentagonal numbers as weights.
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LINKS
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EXAMPLE
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Triangle T(n, k) starts:
[0] 1;
[1] 1, 1;
[2] 1, 6, 6;
[3] 1, 18, 96, 96;
[4] 1, 40, 576, 2976, 2976;
[5] 1, 75, 2226, 29688, 151416, 151416;
[6] 1, 126, 6636, 175680, 2259576, 11449296, 11449296;
[7] 1, 196, 16632, 757800, 18931176, 238623408, 1204566336, 1204566336;
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MAPLE
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T := proc(n, k) option remember; if k = 0 then 1 else if k = n then T(n, k-1)
else (((n - k + 1)*(3*n - 3*k + 2))/2) * T(n, k - 1) + T(n - 1, k) fi fi end:
seq(seq(T(n, k), k = 0..n), n = 0..8);
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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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