%I #11 Oct 26 2018 18:48:14
%S 1,18,210,1980,16467,126126,912338,6332055,42615547,280182355,
%T 1809148533,11517941151,72515126734,452500330899,2803547693199,
%U 17270035728605,105888136423278,646765377652715,3938163632325325,23918395342393710,144963673674486886
%N Number of set partitions of [n] into exactly eight parts such that no part contains two elements with a circular distance less than three.
%H Alois P. Heinz, <a href="/A261484/b261484.txt">Table of n, a(n) for n = 8..1000</a>
%H <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (14,-70,231, -973,2800, -5291,17289, -28574,30709, -127043,26684, -91944,352921, 496104,584696, 276192,-496944, -518400,-518400).
%F G.f.: (720*x^11 +720*x^10 +580*x^9 +2204*x^8 +755*x^7 +1105*x^6 +392*x^5 +262*x^4 +69*x^3 +28*x^2 +4*x+1) *x^8 / ((x-1) *(6*x-1) *(5*x-1) *(3*x-1) *(2*x-1) *(4*x-1) *(x+1) *(x^2+x+1) *(5*x^2+x+1) *(3*x^2+x+1) *(4*x^2+x+1) *(2*x^2+x+1) *(6*x^2+x+1)).
%e a(8) = 1: 1|2|3|4|5|6|7|8.
%e a(9) = 18: 14|2|3|5|6|7|8|9, 15|2|3|4|6|7|8|9, 1|25|3|4|6|7|8|9, 16|2|3|4|5|7|8|9, 1|26|3|4|5|7|8|9, 1|2|36|4|5|7|8|9, 17|2|3|4|5|6|8|9, 1|27|3|4|5|6|8|9, 1|2|37|4|5|6|8|9, 1|2|3|47|5|6|8|9, 1|28|3|4|5|6|7|9, 1|2|38|4|5|6|7|9, 1|2|3|48|5|6|7|9, 1|2|3|4|58|6|7|9, 1|2|39|4|5|6|7|8, 1|2|3|49|5|6|7|8, 1|2|3|4|59|6|7|8, 1|2|3|4|5|69|7|8.
%Y Column k=8 of A261477.
%K nonn,easy
%O 8,2
%A _Alois P. Heinz_, Aug 20 2015