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 A104002 #23 Feb 15 2022 12:57:15
%S A104002 1,2,1,3,4,1,4,12,6,1,5,32,27,8,1,6,80,108,48,10,1,7,192,405,256,75,
%T A104002 12,1,8,448,1458,1280,500,108,14,1,9,1024,5103,6144,3125,864,147,16,1,
%U A104002 10,2304,17496,28672,18750,6480,1372,192,18,1,11,5120,59049,131072
%N A104002 Triangle T(n,k) read by rows: number of permutations in S_n avoiding all k-length patterns that start with 1 except one fixed pattern and containing it exactly once.
%C A104002 T(n+k,k+1) = total number of occurrences of any given letter in all possible n-length words on a k-letter alphabet. For example, with the 2 letter alphabet {0,1} there are 4 possible 2-length words: {00,01,10,11}. The letter 0 occurs 4 times altogether, as does the letter 1. T(4,3) = 4. - _Ross La Haye_, Jan 03 2007
%C A104002 Table T(n,k) = k*n^(k-1) n,k > 0 read by antidiagonals. - _Boris Putievskiy_, Dec 17 2012
%H A104002 Michael De Vlieger, <a href="/A104002/b104002.txt">Table of n, a(n) for n = 2..11176</a> (rows 2 <= n <= 150).
%H A104002 T. Mansour, <a href="https://arxiv.org/abs/math/9911243">Permutations containing and avoiding certain patterns</a>, arXiv:math/9911243 [math.CO], 1999-2000.
%H A104002 Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations Integer Sequences And Pairing Functions</a>, arXiv:1212.2732 [math.CO], 2012.
%H A104002 Franck Ramaharo, <a href="https://arxiv.org/abs/1805.10680">A generating polynomial for the pretzel knot</a>, arXiv:1805.10680 [math.CO], 2018.
%F A104002 T(n, k) = (n-k+1) * (k-1)^(n-k), k<=n.
%F A104002 As a linear array, the sequence is a(n) = A004736(n)*A002260(n)^(A004736(n)-1) or a(n) = ((t*t+3*t+4)/2-n)*(n-(t*(t+1)/2))^((t*t+3*t+4)/2-n-1), where t=floor((-1+sqrt(8*n-7))/2). - _Boris Putievskiy_, Dec 17 2012
%e A104002 Triangle begins:
%e A104002 1;
%e A104002 2, 1;
%e A104002 3, 4, 1;
%e A104002 4, 12, 6, 1;
%e A104002 5, 32, 27, 8, 1;
%e A104002 6, 80, 108, 48, 10, 1;
%e A104002 7, 192, 405, 256, 75, 12, 1;
%e A104002 8, 448, 1458, 1280, 500, 108, 14, 1;
%t A104002 Table[(n - k + 1) (k - 1)^(n - k), {n, 2, 12}, {k, 2, n}] // Flatten (* _Michael De Vlieger_, Aug 22 2018 *)
%Y A104002 Cf. Left-edge columns include A001787, A027471, A002697, A053464, A053469, A027473, A053539, A053540, A053541, A081127, A081128.
%K A104002 nonn,tabl
%O A104002 2,2
%A A104002 _Ralf Stephan_, Feb 26 2005