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A365672
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Triangle read by rows. T(n, k) = 1 if k = 0, equals T(n, k-1) if k = n, and otherwise is (n - k + 1) * (2 * (n - k) + 1) * T(n, k - 1) + T(n - 1, k).
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2
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1, 1, 1, 1, 7, 7, 1, 22, 139, 139, 1, 50, 889, 5473, 5473, 1, 95, 3549, 58708, 357721, 357721, 1, 161, 10794, 360940, 5771821, 34988647, 34988647, 1, 252, 27426, 1595110, 50434901, 791512162, 4784061619, 4784061619
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OFFSET
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0,5
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COMMENTS
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This triangle is described by Peter Bala (see link).
This a weighted generalized Catalan triangle (A365673) with the hexagonal 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, 7, 7;
[3] 1, 22, 139, 139;
[4] 1, 50, 889, 5473, 5473;
[5] 1, 95, 3549, 58708, 357721, 357721;
[6] 1, 161, 10794, 360940, 5771821, 34988647, 34988647;
[7] 1, 252, 27426, 1595110, 50434901, 791512162, 4784061619, 4784061619;
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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) * (2 * (n - k) + 1) * T(n, k - 1) + T(n - 1, k) fi fi end:
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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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