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A322881 Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals eight.

%I A322881 #5 Dec 29 2018 17:44:13
%S A322881 0,1,131,2837,36733,392532,3862958,36745885,346270455,3276723147,
%T A322881 31384368348,305668217577,3035028866706,30761374688048,
%U A322881 318435571825333,3367380704425616,36376061350280633,401367264163810215,4522617803400779891,52030240381937090624
%N A322881 Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals eight.
%H A322881 Alois P. Heinz, <a href="/A322881/b322881.txt">Table of n, a(n) for n = 8..580</a>
%H A322881 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A322881 a(n) = A287258(n) - A287257(n).
%p A322881 b:= proc(n, k, m, l) option remember; `if`(n<1, 1,
%p A322881      `if`(l-n>k, 0, b(n-1, k, m+1, n))+m*b(n-1, k, m, l))
%p A322881     end:
%p A322881 A:= (n, k)-> b(n-1, min(k, n-1), 1, n):
%p A322881 a:= n-> (k-> A(n, k)-A(n, k-1))(8):
%p A322881 seq(a(n), n=8..30);
%Y A322881 Column k=8 of A287215.
%Y A322881 Cf. A287257, A287258.
%K A322881 nonn
%O A322881 8,3
%A A322881 _Alois P. Heinz_, Dec 29 2018