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A229003 Total sum of cubed lengths of ascending runs in all permutations of [n].

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