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%I #16 May 21 2024 08:46:27
%S 1,2,10,60,408,3120,26640,252000,2620800,29756160,366508800,
%T 4869849600,69455232000,1058593536000,17174123366400,295534407168000,
%U 5377157001216000,103149354147840000,2080771454361600000
%N a(n) = (n^2+1)*n!.
%C Main diagonal of A082037
%C 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 a(n) is also the number of distinct planar embeddings of the (n+1)-Sierpinski gasket graph. - _Eric W. Weisstein_, May 21 2024
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PlanarEmbedding.html">Planar Embedding</a>.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SierpinskiGasketGraph.html">Sierpinski Gasket Graph</a>.
%F a(n) = A002522(n)*A000142(n).
%F (n^2-2*n+2)*a(n) -n*(n^2+1)*a(n-1)=0. - _R. J. Mathar_, Dec 03 2014
%Y Cf. A018932. [From _R. J. Mathar_, Dec 15 2008]
%Y Cf. A000142, A002522, A082037.
%K easy,nonn,changed
%O 0,2
%A _Paul Barry_, Apr 02 2003
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