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%I #11 Aug 26 2019 14:56:11
%S 0,1,10,66,426,2964,22818,195000,1842234,19120260,216604194,
%T 2662063728,35297775930,502460232684,7644691295970,123824090015544,
%U 2127644969464698,38659776477571860,740692592536389474,14924674961053224000,315523813278300959994
%N Total sum of cubed lengths of ascending runs in all permutations of [n].
%H Alois P. Heinz, <a href="/A229003/b229003.txt">Table of n, a(n) for n = 0..200</a>
%F E.g.f.: (6*exp(x)*(x-1)+x+6)/(x-1)^2.
%F a(n) ~ n! * 7*n. - _Vaclav Kotesovec_, Sep 12 2013
%p a:= proc(n) option remember; `if`(n<3, [0, 1, 10][n+1],
%p ((2*n^2-3*n-1)*a(n-1) -(n-1)*(n^2-2)*a(n-2)
%p +(n-2)*(n-1)^2*a(n-3) )/(n-2))
%p end:
%p seq(a(n), n=0..25);
%t With[{nn=20},CoefficientList[Series[(6 Exp[x](x-1)+x+6)/(x-1)^2,{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Aug 26 2019 *)
%Y Column k=3 of A229001.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Sep 10 2013
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