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 A082042 #18 Aug 27 2025 07:27:31 %S A082042 1,2,10,60,408,3120,26640,252000,2620800,29756160,366508800, %T A082042 4869849600,69455232000,1058593536000,17174123366400,295534407168000, %U A082042 5377157001216000,103149354147840000,2080771454361600000 %N A082042 a(n) = (n^2+1)*n!. %C A082042 Main diagonal of A082037 %C A082042 a(n) = total number of runs when each permutation on [n+1] is split into maximal monotone runs. (A monotone run is a sequence of consecutive entries whose differences are all 1 or all -1. Example: 34-1-765-2 contributes 4 runs to a(6) as indicated.) - _David Callan_, Nov 16 2003 %C A082042 a(n) is also the number of distinct planar embeddings of the (n+1)-Sierpinski gasket graph. - _Eric W. Weisstein_, May 21 2024 %H A082042 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PlanarEmbedding.html">Planar Embedding</a>. %H A082042 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SierpinskiGasketGraph.html">Sierpinski Gasket Graph</a>. %F A082042 a(n) = A002522(n)*A000142(n). %F A082042 D-finite with recurrence (n^2-2*n+2)*a(n) -n*(n^2+1)*a(n-1)=0. - _R. J. Mathar_, Dec 03 2014 %Y A082042 Cf. A018932. [From _R. J. Mathar_, Dec 15 2008] %Y A082042 Cf. A000142, A002522, A082037. %K A082042 easy,nonn,changed %O A082042 0,2 %A A082042 _Paul Barry_, Apr 02 2003