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 A111933 #36 Feb 13 2022 23:16:43 %S A111933 1,1,1,1,2,2,1,3,7,6,1,4,15,35,24,1,5,26,105,228,120,1,6,40,234,947, %T A111933 1834,720,1,7,57,440,2696,10472,17582,5040,1,8,77,741,6170,37919, %U A111933 137337,195866,40320,1,9,100,1155,12244,105315,630521,2085605,2487832,362880 %N A111933 Triangle read by rows, generated from Stirling cycle numbers. %C A111933 Let M = the infinite lower triangular matrix of Stirling cycle numbers (A008275). Perform M^n * [1, 0, 0, 0, ...] forming an array. Antidiagonals of that array become the rows of this triangle. %H A111933 Seiichi Manyama, <a href="/A111933/b111933.txt">Antidiagonals n = 1..140, flattened</a> %e A111933 Row 5 of the triangle = 1, 4, 15, 35, 24; generated from M^n * [1,0,0,0,...] (n = 1 through 5); then take antidiagonals. %e A111933 Terms in the array, first few rows are: %e A111933 1, 1, 2, 6, 24, 120, ... %e A111933 1, 2, 7, 35, 228, 1834, ... %e A111933 1, 3, 15, 105, 947, 10472, ... %e A111933 1, 4, 26, 234, 2697, 37919, ... %e A111933 1, 5, 40, 440, 6170, 105315, ... %e A111933 1, 6, 57, 741, 12244, 245755, ... %e A111933 ... %e A111933 First few rows of the triangle are: %e A111933 1; %e A111933 1, 1; %e A111933 1, 2, 2; %e A111933 1, 3, 7, 6; %e A111933 1, 4, 15, 35, 24; %e A111933 1, 5, 26, 105, 228, 120; %e A111933 1, 6, 40, 234, 947, 1834, 720; %e A111933 ... %Y A111933 Row 1..7 give A000142(n-1), A003713, A000268, A000310, A000359, A000406, A001765. %Y A111933 Column 3 of the array = A005449. %Y A111933 Column 4 of the array = A094952. %Y A111933 Cf. A008275, A302358. %K A111933 nonn,tabl %O A111933 1,5 %A A111933 _Gary W. Adamson_, Aug 21 2005 %E A111933 a(28), a(36) and a(45) corrected by _Seiichi Manyama_, Feb 11 2022