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%I #12 Sep 13 2013 19:55:17
%S 0,1,66,992,9846,86782,765506,7112202,71000398,766053422,8931231882,
%T 112221527986,1514394506102,21867699419238,336675784490002,
%U 5508056657818442,95455624774115166,1747299831395273182,33693372749353108058,682771622138237836962
%N Total sum of the 6th powers of lengths of ascending runs in all permutations of [n].
%H Alois P. Heinz, <a href="/A228996/b228996.txt">Table of n, a(n) for n = 0..200</a>
%F E.g.f.: (exp(x)*(30*x^4+60*x^3+60*x^2-60*x+62)-x-62)/(x-1)^2.
%F a(n) ~ n! * (152*exp(1)-63)*n. - _Vaclav Kotesovec_, Sep 12 2013
%p a:= proc(n) option remember; `if`(n<3, [0, 1, 66][n+1],
%p ((30*n^5-225*n^4+690*n^3-975*n^2+512*n+31)*a(n-1)
%p -(n-1)*(15*n^5-90*n^4+255*n^3-330*n^2+121*n+62)*a(n-2)
%p +(15*n^6-105*n^5+315*n^4-525*n^3+511*n^2-273*n+62)*a(n-3))/
%p (15*n^4-120*n^3+375*n^2-540*n+301))
%p end:
%p seq(a(n), n=0..30);
%Y Column k=6 of A229001.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Sep 10 2013
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