%I #8 Aug 20 2015 23:20:20
%S 1,7,42,210,985,4400,18944,80067,333431,1372364,5607350,22788432,
%T 92221903,372094575,1498066156,6021295070,24172138331,96949953648,
%U 388584438750,1556689868075,6233817797545,24956454853128,99889360100264,399748052249200,1599564125648941
%N Number of set partitions of [n] into exactly six parts such that no part contains two elements with a circular distance less than three.
%H Alois P. Heinz, <a href="/A261482/b261482.txt">Table of n, a(n) for n = 6..1000</a>
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (5,-5,25,-74,-16,-185,205,401,737,440,-380,-576,-576).
%F G.f.: (24*x^7+24*x^6+9*x^5+44*x^4+10*x^3+12*x^2+2*x+1) *x^6 / ((x-1) *(3*x-1) *(2*x-1) *(4*x-1) *(x+1) *(x^2+x+1) *(3*x^2+x+1) *(2*x^2+x+1) *(4*x^2+x+1)).
%e a(6) = 1: 1|2|3|4|5|6.
%e a(7) = 7: 14|2|3|5|6|7, 15|2|3|4|6|7, 1|25|3|4|6|7, 1|26|3|4|5|7, 1|2|36|4|5|7, 1|2|37|4|5|6, 1|2|3|47|5|6.
%e a(8) = 42: 14|25|3|6|7|8, 14|26|3|5|7|8, 14|2|36|5|7|8, 14|27|3|5|6|8, 14|2|37|5|6|8, 14|2|38|5|6|7, 14|2|3|58|6|7, 15|26|3|4|7|8, 15|2|36|4|7|8, 15|27|3|4|6|8, 15|2|37|4|6|8, 15|2|3|47|6|8, 15|2|38|4|6|7, 15|2|3|48|6|7, 16|25|3|4|7|8, 1|25|36|4|7|8, 1|25|37|4|6|8, 1|25|3|47|6|8, 1|25|38|4|6|7, 1|25|3|48|6|7, 16|27|3|4|5|8, 16|2|37|4|5|8, 16|2|3|47|5|8, 16|2|38|4|5|7, 16|2|3|48|5|7, 16|2|3|4|58|7, 1|26|37|4|5|8, 1|26|3|47|5|8, 1|26|38|4|5|7, 1|26|3|48|5|7, 1|26|3|4|58|7, 1|27|36|4|5|8, 1|2|36|47|5|8, 1|2|36|48|5|7, 1|2|36|4|58|7, 1|27|38|4|5|6, 1|27|3|48|5|6, 1|27|3|4|58|6, 1|2|37|48|5|6, 1|2|37|4|58|6, 1|2|38|47|5|6, 1|2|3|47|58|6.
%Y Column k=6 of A261477.
%K nonn,easy
%O 6,2
%A _Alois P. Heinz_, Aug 20 2015