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 A112858 #8 Dec 05 2016 02:41:24 %S A112858 1,2,3,3,11,12,4,32,132,60,5,84,1152,2664,360,6,208,9072,93312,80640, %T A112858 2520,7,496,67392,2944512,14169600,3412800,20160,8,1152,482112, %U A112858 87588864,2239488000,3608064000,192326400,181440,9,2624,3359232,2508226560 %N A112858 Table read by antidiagonals: T(n,k) = count of increasing runs in strings of length n*k formed by concatenating k permutations of [n]. %C A112858 The first column T(n,1) is A001710(n+1), i.e., (n+1)!/2. The 2nd column T(n,2) is the outer diagonal of triangle A122823. %F A112858 T(n,k) = (k(n+1)/2 - (k-1)(n-1)/2n) * (n!)^k. %e A112858 Table begins: %e A112858 1 2 3 4 ... %e A112858 3 11 32 84 ... %e A112858 12 132 1152 9072 ... %e A112858 60 2664 93312 2944512 ... %e A112858 ... %e A112858 Example: Take the permutations of [2], namely, 12 and 21, and form all possible strings that are concatenations of 2 of these permutations. These are 1212, 1221, 2112, 2121 with 2, 3, 3, 3 increasing runs respectively. T(2,2) = 2 + 3 + 3 + 3 = 11. %Y A112858 Cf. A001710, A110952, A122823. %K A112858 easy,nonn,tabl %O A112858 1,2 %A A112858 _David Scambler_, Nov 22 2006