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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

%I #5 Oct 01 2023 07:31:54

%S 1,1,1,1,6,6,1,18,96,96,1,40,576,2976,2976,1,75,2226,29688,151416,

%T 151416,1,126,6636,175680,2259576,11449296,11449296,1,196,16632,

%U 757800,18931176,238623408,1204566336,1204566336

%N 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.

%C This a weighted generalized Catalan triangle (A365673) with the pentagonal numbers as weights.

%e Triangle T(n, k) starts:

%e [0] 1;

%e [1] 1, 1;

%e [2] 1, 6, 6;

%e [3] 1, 18, 96, 96;

%e [4] 1, 40, 576, 2976, 2976;

%e [5] 1, 75, 2226, 29688, 151416, 151416;

%e [6] 1, 126, 6636, 175680, 2259576, 11449296, 11449296;

%e [7] 1, 196, 16632, 757800, 18931176, 238623408, 1204566336, 1204566336;

%p T := proc(n, k) option remember; if k = 0 then 1 else if k = n then T(n, k-1)

%p else (((n - k + 1)*(3*n - 3*k + 2))/2) * T(n, k - 1) + T(n - 1, k) fi fi end:

%p seq(seq(T(n, k), k = 0..n), n = 0..8);

%Y Cf. A000326, A126151 (main diagonal), A365673.

%K nonn,tabl

%O 0,5

%A _Peter Luschny_, Oct 01 2023

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Last modified August 11 10:58 EDT 2024. Contains 375068 sequences. (Running on oeis4.)