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A287278 Number of set partitions of [n] such that for each block all absolute differences between consecutive elements are <= six.

%I A287278 #9 Dec 26 2018 15:02:34
%S A287278 1,1,2,5,15,52,203,877,3937,18162,85347,405803,1942918,9339084,
%T A287278 45003444,217201380,1049271992,5071767524,24523356660,118602078194,
%U A287278 573667951966,2774998925735,13424115897227,64941326312858,314169695256551,1519889795069445,7352969270282127
%N A287278 Number of set partitions of [n] such that for each block all absolute differences between consecutive elements are <= six.
%H A287278 Alois P. Heinz, <a href="/A287278/b287278.txt">Table of n, a(n) for n = 0..1000</a>
%H A287278 Pierpaolo Natalini, Paolo Emilio Ricci, <a href="https://doi.org/10.3390/axioms7040071">New Bell-Sheffer Polynomial Sets</a>, Axioms 2018, 7(4), 71.
%H A287278 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A287278 G.f.: -(x^31 +2*x^30 +3*x^29 +4*x^28 +6*x^27 -24*x^26 -46*x^25 -60*x^24 -81*x^23 -129*x^22 +156*x^21 +265*x^20 +224*x^19 +350*x^18 +617*x^17 -425*x^16 -531*x^15 -161*x^14 -567*x^13 -806*x^12 +462*x^11 +401*x^10 +85*x^9 +198*x^8 +227*x^7 -185*x^6 -35*x^5 -4*x^4 -5*x^3 -4*x^2 +6*x-1) / (x^32 +x^31 +x^30 +x^29 +x^28 -32*x^27 -24*x^26 -15*x^25 -23*x^24 -23*x^23 +329*x^22 +141*x^21 -20*x^20 +164*x^19 +101*x^18 -1243*x^17 -175*x^16 +277*x^15 -495*x^14 +8*x^13 +1536*x^12 +17*x^11 -235*x^10 +121*x^9 -115*x^8 -447*x^7 +152*x^6 +32*x^5 +x^4 +5*x^3 +9*x^2 -7*x+1).
%F A287278 a(n) = A287214(n,6).
%F A287278 a(n) = A000110(n) for n <= 7.
%Y A287278 Column k=6 of A287214.
%Y A287278 Cf. A000110.
%K A287278 nonn,easy
%O A287278 0,3
%A A287278 _Alois P. Heinz_, May 22 2017