%I #8 Apr 08 2018 17:04:40
%S 0,6,304,3159,16896,62500,182736,453789,999424,2007666,3750000,
%T 6603091,11073024,17822064,27697936,41765625,61341696,88031134,
%U 123766704,170850831,232000000,310391676,409713744,534216469,688766976,878906250,1110908656,1391843979
%N a(n) = n^5*(7*n+5)/2.
%C Number of ascending runs in {1,...,n}^6.
%H Alois P. Heinz, <a href="/A229148/b229148.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 35, -35, 21, -7, 1).
%F G.f.: -(x^5+137*x^4+957*x^3+1157*x^2+262*x+6)*x/(x-1)^7.
%p a:= n-> n^5*(7*n+5)/2:
%p seq(a(n), n=0..40);
%t Table[n^5(7*n+5)/2,{n,0,30}] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,6,304,3159,16896,62500,182736},30] (* _Harvey P. Dale_, Apr 07 2018 *)
%Y Row n=6 of A229079.
%K nonn,easy
%O 0,2
%A _Alois P. Heinz_, Sep 15 2013