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%I #6 May 26 2017 20:58:27
%S 1,1,2,5,15,52,203,824,3407,14176,58954,244412,1010802,4167621,
%T 17133558,70278017,287797888,1177218237,4811244031,19651589669,
%U 80234989720,327503437323,1336574600154,5454075504109,22254465906164,90801509373219,370472833209387
%N Number of set partitions of [n] such that all absolute differences between least elements of consecutive blocks and between consecutive elements within the blocks are not larger than five.
%H Alois P. Heinz, <a href="/A287584/b287584.txt">Table of n, a(n) for n = 0..1000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F G.f.: -(16*x^55 +40*x^54 +8*x^53 +74*x^52 -5*x^51 -318*x^50 -184*x^49 -329*x^48 -142*x^47 -724*x^46 -4295*x^45 +135*x^44 +10219*x^43 +11230*x^42 +17694*x^41 -9835*x^40 -58571*x^39 -44920*x^38 -18846*x^37 +77331*x^36 +137586*x^35 -2726*x^34 -66412*x^33 -120019*x^32 -106707*x^31 +110373*x^30 +61244*x^29 -89340*x^28 -166963*x^27 -241737*x^26 -18801*x^25 +183341*x^24 +76875*x^23 -44809*x^22 -194064*x^21 -276159*x^20 -117373*x^19 -3527*x^18 +50167*x^17 +68672*x^16 +6577*x^15 -20654*x^14 -18383*x^13 -13866*x^12 -2815*x^11 +2840*x^10 +1096*x^9 +484*x^8 +288*x^7 -290*x^6 -31*x^5 -4*x^4 -3*x^3 -2*x^2 +5*x -1) / ((x +1)*(x^5 -2*x^3 -2*x +1)*(16*x^40 +8*x^39 -8*x^38 -6*x^37 -25*x^36 -20*x^35 +20*x^34 -447*x^33 -222*x^32 -535*x^31 -399*x^30 +3024*x^29 +1695*x^28 +1438*x^27 +444*x^26 -7664*x^25 -2469*x^24 +1957*x^23 +290*x^22 -50*x^21 -6904*x^20 -7025*x^19 +2502*x^18 +2901*x^17 +352*x^16 -822*x^15 -8224*x^14 -7130*x^13 -2351*x^12 +680*x^11 +2679*x^10 +2620*x^9 +1264*x^8 +408*x^7 +62*x^6 -105*x^5 -48*x^4 -17*x^3 -5*x^2 -x +1)*(x -1)^2*(x^4 +x^3 +x^2 +x -1)^2).
%F a(n) = A000110(n) for n <= 6.
%Y Column k=5 of A287417.
%Y Cf. A000110.
%K nonn,easy
%O 0,3
%A _Alois P. Heinz_, May 26 2017
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