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A322879 Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals six.

%I A322879 #4 Dec 29 2018 15:50:15
%S A322879 0,1,35,413,3709,30396,242366,1934021,15653524,129267234,1091892025,
%T A322879 9444993005,83722879838,760771479660,7087056828919,67674638461955,
%U A322879 662248199987728,6638947646238102,68153572265860585,716151632403862252,7699437833837232406
%N A322879 Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals six.
%H A322879 Alois P. Heinz, <a href="/A322879/b322879.txt">Table of n, a(n) for n = 6..581</a>
%H A322879 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A322879 a(n) = A287256(n) - A287255(n).
%p A322879 b:= proc(n, k, m, l) option remember; `if`(n<1, 1,
%p A322879      `if`(l-n>k, 0, b(n-1, k, m+1, n))+m*b(n-1, k, m, l))
%p A322879     end:
%p A322879 A:= (n, k)-> b(n-1, min(k, n-1), 1, n):
%p A322879 a:= n-> (k-> A(n, k)-A(n, k-1))(6):
%p A322879 seq(a(n), n=6..30);
%Y A322879 Column k=6 of A287215.
%Y A322879 Cf. A287255, A287256.
%K A322879 nonn
%O A322879 6,3
%A A322879 _Alois P. Heinz_, Dec 29 2018