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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
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
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.)