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%I #9 Aug 20 2015 23:19:57
%S 1,12,102,720,4587,27326,155571,858023,4623388,24488768,128053146,
%T 663054996,3407483161,17409523182,88545747922,448749879028,
%U 2267921345677,11436557773522,57571373075875,289413549581585,1453301573317896,7291464343122268,36557211011698580
%N Number of set partitions of [n] into exactly seven parts such that no part contains two elements with a circular distance less than three.
%H Alois P. Heinz, <a href="/A261483/b261483.txt">Table of n, a(n) for n = 7..1000</a>
%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (9,-25,70,-299,405,-746,2795,-19,3758,-7633,-12165,-17481,-9272,11804,14400,14400).
%F G.f.: -(120*x^9 +120*x^8 +71*x^7 +296*x^6 +86*x^5 +116*x^4 +32*x^3 +19*x^2 +3*x+1) *x^7 / ((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)).
%e a(7) = 1: 1|2|3|4|5|6|7.
%e a(8) = 12: 14|2|3|5|6|7|8, 15|2|3|4|6|7|8, 1|25|3|4|6|7|8, 16|2|3|4|5|7|8, 1|26|3|4|5|7|8, 1|2|36|4|5|7|8, 1|27|3|4|5|6|8, 1|2|37|4|5|6|8, 1|2|3|47|5|6|8, 1|2|38|4|5|6|7, 1|2|3|48|5|6|7, 1|2|3|4|58|6|7.
%Y Column k=7 of A261477.
%K nonn,easy
%O 7,2
%A _Alois P. Heinz_, Aug 20 2015
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