This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A356263 #15 Aug 04 2022 14:57:47 %S A356263 1,0,1,0,2,1,0,3,9,1,0,5,41,24,1,0,8,150,247,55,1,0,14,494,1746,1074, %T A356263 118,1,0,24,1537,10126,13110,4050,245,1,0,43,4642,52129,122521,79396, %U A356263 14111,500,1,0,77,13745,248494,967644,1126049,425471,46833,1011,1 %N A356263 Triangle read by rows. The reduced triangle of the partition triangle of irreducible permutations (A356262). T(n, k) for n >= 1 and 0 <= k < n. %C A356263 The triangle can be seen as Euler's triangle A008292 restricted to irreducible permutations. %C A356263 See the comments in A356116 for the definition of the terms 'partition triangle' and 'reduced partition triangle'. The reduction procedure is formalized in the Sage program in A356116. %H A356263 Peter Luschny, <a href="https://github.com/PeterLuschny/PermutationsWithLehmer/blob/main/PermutationsWithLehmer.ipynb">Permutations with Lehmer</a>, a SageMath Jupyter Notebook. %e A356263 [1] [1] %e A356263 [2] [0, 1] %e A356263 [3] [0, 2, 1] %e A356263 [4] [0, 3, 9, 1] %e A356263 [5] [0, 5, 41, 24, 1] %e A356263 [6] [0, 8, 150, 247, 55, 1] %e A356263 [7] [0, 14, 494, 1746, 1074, 118, 1] %e A356263 [8] [0, 24, 1537, 10126, 13110, 4050, 245, 1] %e A356263 [9] [0, 43, 4642, 52129, 122521, 79396, 14111, 500, 1] %e A356263 [10][0, 77, 13745, 248494, 967644, 1126049, 425471, 46833, 1011, 1] %e A356263 . %e A356263 The 5 irreducible permutations counted with T(5, 2) are 23451, 51234, 31524, 34512, and 45123. %o A356263 (SageMath) # Uses function 'reduce_partition_triangle' from A356116. %o A356263 reduce_partition_triangle(A356262_row, 8) %Y A356263 Cf. A356262 (partition triangle), A007059 (column 2), A003319 (row sums), A356114 (subdiagonal). %Y A356263 Cf. A008292, A356116. %K A356263 nonn,tabl %O A356263 1,5 %A A356263 _Peter Luschny_, Aug 01 2022