cp's OEIS Frontend

A228996 Total sum of the 6th powers of lengths of ascending runs in all permutations of [n].

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