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Number of set partitions of [n] such that for each block all absolute differences between consecutive elements are <= seven.
4

%I #10 Dec 26 2018 15:02:41

%S 1,1,2,5,15,52,203,877,4140,20270,102004,523700,2726840,14332663,

%T 75789343,402290332,2140945657,11413941169,60921661218,325417158033,

%U 1739114057259,9297387238139,49715367098205,265879355474309,1422070344597675,7606514013820659

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

%H Alois P. Heinz, <a href="/A287279/b287279.txt">Table of n, a(n) for n = 0..1000</a>

%H Alois P. Heinz, <a href="/A287279/a287279.txt">G.f. for A287279</a>

%H 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 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

%F G.f.: see link above.

%F a(n) = A287214(n,7).

%F a(n) = A000110(n) for n <= 8.

%Y Column k=7 of A287214.

%Y Cf. A000110.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, May 22 2017