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 A218577 #33 Nov 26 2018 17:12:49 %S A218577 1,1,1,1,3,1,1,7,6,1,1,15,25,11,1,1,31,90,74,20,1,1,63,301,402,209,37, %T A218577 1,1,127,966,1951,1629,590,70,1,1,255,3025,8869,10839,6430,1685,135,1, %U A218577 1,511,9330,38720,65720,56878,25313,4870,264,1 %N A218577 Triangle read by rows: T(n,k) is the number of ascent sequences of length n with maximal element k-1. %C A218577 Row sums are A022493. %C A218577 Second column is A000225 (2^n - 1). %C A218577 Third column appears to be A000392 (Stirling numbers S(n,3)). %C A218577 Second diagonal (from the right) appears to be A006127 (2^n + n). %H A218577 Joerg Arndt and Alois P. Heinz, <a href="/A218577/b218577.txt">Rows n = 1..141, flattened</a> (first 15 rows from Joerg Arndt) %H A218577 Mireille Bousquet-Mélou, Anders Claesson, Mark Dukes, Sergey Kitaev, <a href="http://arxiv.org/abs/0806.0666">(2+2)-free posets, ascent sequences and pattern avoiding permutations</a>, arXiv:0806.0666 [math.CO], 2008-2009. %H A218577 William Y. C. Chen, Alvin Y.L. Dai, Theodore Dokos, Tim Dwyer and Bruce E. Sagan, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v20i1p76">On 021-Avoiding Ascent Sequences, The Electronic Journal of Combinatorics</a> Volume 20, Issue 1 (2013), #P76. %e A218577 Triangle starts: %e A218577 1; %e A218577 1, 1; %e A218577 1, 3, 1; %e A218577 1, 7, 6, 1; %e A218577 1, 15, 25, 11, 1; %e A218577 1, 31, 90, 74, 20, 1; %e A218577 1, 63, 301, 402, 209, 37, 1; %e A218577 1, 127, 966, 1951, 1629, 590, 70, 1; %e A218577 1, 255, 3025, 8869, 10839, 6430, 1685, 135, 1; %e A218577 1, 511, 9330, 38720, 65720, 56878, 25313, 4870, 264, 1; %e A218577 1, 1023, 28501, 164676, 376114, 444337, 292695, 99996, 14209, 521, 1; %e A218577 ... %e A218577 The 53 ascent sequences of length 5 are (dots for zeros): %e A218577 [ #] ascent-seq. #max digit %e A218577 [ 1] [ . . . . . ] 0 %e A218577 [ 2] [ . . . . 1 ] 1 %e A218577 [ 3] [ . . . 1 . ] 1 %e A218577 [ 4] [ . . . 1 1 ] 1 %e A218577 [ 5] [ . . . 1 2 ] 2 %e A218577 [ 6] [ . . 1 . . ] 1 %e A218577 [ 7] [ . . 1 . 1 ] 1 %e A218577 [ 8] [ . . 1 . 2 ] 2 %e A218577 [ 9] [ . . 1 1 . ] 1 %e A218577 [10] [ . . 1 1 1 ] 1 %e A218577 [11] [ . . 1 1 2 ] 2 %e A218577 [12] [ . . 1 2 . ] 2 %e A218577 [13] [ . . 1 2 1 ] 2 %e A218577 [14] [ . . 1 2 2 ] 2 %e A218577 [15] [ . . 1 2 3 ] 3 %e A218577 [16] [ . 1 . . . ] 1 %e A218577 [17] [ . 1 . . 1 ] 1 %e A218577 [18] [ . 1 . . 2 ] 2 %e A218577 [19] [ . 1 . 1 . ] 1 %e A218577 [20] [ . 1 . 1 1 ] 1 %e A218577 [21] [ . 1 . 1 2 ] 2 %e A218577 [22] [ . 1 . 1 3 ] 3 %e A218577 [23] [ . 1 . 2 . ] 2 %e A218577 [24] [ . 1 . 2 1 ] 2 %e A218577 [25] [ . 1 . 2 2 ] 2 %e A218577 [26] [ . 1 . 2 3 ] 3 %e A218577 [27] [ . 1 1 . . ] 1 %e A218577 [28] [ . 1 1 . 1 ] 1 %e A218577 [29] [ . 1 1 . 2 ] 2 %e A218577 [...] %e A218577 [49] [ . 1 2 3 . ] 3 %e A218577 [50] [ . 1 2 3 1 ] 3 %e A218577 [51] [ . 1 2 3 2 ] 3 %e A218577 [52] [ . 1 2 3 3 ] 3 %e A218577 [53] [ . 1 2 3 4 ] 4 %e A218577 There is 1 sequence with maximum zero, 15 with maximum one, etc., %e A218577 therefore the fifth row is 1, 15, 25, 11, 1. %Y A218577 Cf. A022493 (number of ascent sequences), A137251 (ascent sequences with k ascents), A175579 (ascent sequences with k zeros). %Y A218577 Cf. A218579 (ascent sequences with last zero at position k-1), A218580 (ascent sequences with first occurrence of the maximal value at position k-1), A218581 (ascent sequences with last occurrence of the maximal value at position k-1). %K A218577 nonn,tabl %O A218577 1,5 %A A218577 _Joerg Arndt_, Nov 03 2012