%I #14 Oct 24 2023 06:15:12

%S 0,8,1600,37179,352256,2031250,8538048,28824005,82837504,210450636,

%T 485000000,1032820063,2060328960,3890408054,7009998016,12131015625,

%U 20266876928,32827093840,51732592704,79554584771,119680000000,176506677018,255671683520,364316322829

%N a(n) = n^7*(9*n+7)/2.

%C Number of ascending runs in {1,...,n}^8.

%H Alois P. Heinz, <a href="/A229150/b229150.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).

%F G.f.: -(x^7+695*x^6+15570*x^5+65998*x^4+74573*x^3+23067*x^2+1528*x+8)*x/ (x-1)^9.

%p a:= n-> n^7*(9*n+7)/2:

%p seq(a(n), n=0..40);

%t A229150[n_]:=n^7(9n+7)/2;Array[A229150,30,0] (* _Paolo Xausa_, Oct 24 2023 *)

%Y Row n=8 of A229079.

%K nonn,easy

%O 0,2

%A _Alois P. Heinz_, Sep 15 2013