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A365674
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Triangle read by rows. T(n, k) = ((n - k + 1)*(n - k + 2)/2) * T(n, k - 1) + T(n - 1, k) for 0 < k < n, T(n, 0) = 1 and T(n, n) = T(n, n - 1) for n > 0.
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1
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1, 1, 1, 1, 4, 4, 1, 10, 34, 34, 1, 20, 154, 496, 496, 1, 35, 504, 3520, 11056, 11056, 1, 56, 1344, 16960, 112816, 349504, 349504, 1, 84, 3108, 63580, 748616, 4841200, 14873104, 14873104, 1, 120, 6468, 199408, 3739736, 42238560, 268304464, 819786496, 819786496
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OFFSET
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0,5
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COMMENTS
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This triangle is associated to the case n = 3 of A365673 and has as weight function the triangular numbers A000217. The numbers on its main diagonal are the reduced tangent numbers A002105. For details see A365673.
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LINKS
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EXAMPLE
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[0] 1;
[1] 1, 1;
[2] 1, 4, 4;
[3] 1, 10, 34, 34;
[4] 1, 20, 154, 496, 496;
[5] 1, 35, 504, 3520, 11056, 11056;
[6] 1, 56, 1344, 16960, 112816, 349504, 349504;
[7] 1, 84, 3108, 63580, 748616, 4841200, 14873104, 14873104;
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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)*(n - k + 2)/2) * T( n, k - 1) + T( n - 1, k) fi fi end:
seq(print(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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