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

%I #12 Dec 26 2018 15:02:47

%S 1,1,2,5,15,52,203,877,4140,21147,111835,607726,3372147,19006265,

%T 108345829,622553137,3596571484,20854506433,121247283115,706276123051,

%U 4119684344466,24052768332415,140525287140277,821384370939660,4802655803213444,28087804863005024

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

%H Alois P. Heinz, <a href="/A287280/b287280.txt">Table of n, a(n) for n = 0..1000</a>

%H Alois P. Heinz, <a href="/A287280/a287280.txt">G.f. for A287280</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,8).

%F a(n) = A000110(n) for n <= 9.

%Y Column k=8 of A287214.

%Y Cf. A000110.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, May 22 2017