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 A366138 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. 1
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS This a weighted generalized Catalan triangle (A365673) with the pentagonal numbers as weights. LINKS Table of n, a(n) for n=0..35. EXAMPLE 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; MAPLE 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); CROSSREFS Cf. A000326, A126151 (main diagonal), A365673. Sequence in context: A105817 A093313 A098267 * A122193 A348622 A098369 Adjacent sequences: A366135 A366136 A366137 * A366139 A366140 A366141 KEYWORD nonn,tabl AUTHOR Peter Luschny, Oct 01 2023 STATUS approved

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Last modified July 24 02:45 EDT 2024. Contains 374575 sequences. (Running on oeis4.)