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A322878 Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals five.

%I A322878 #8 May 05 2020 04:28:38
%S A322878 0,1,19,171,1293,9320,66992,488526,3637440,27735903,216992278,
%T A322878 1743777862,14401360577,122242150172,1066284279026,9554869690126,
%U A322878 87923414758506,830459368379431,8047463255217118,79967170844047637,814439368083686232,8497321384591725159
%N A322878 Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals five.
%H A322878 Alois P. Heinz, <a href="/A322878/b322878.txt">Table of n, a(n) for n = 5..582</a>
%H A322878 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A322878 a(n) = A287255(n) - A287254(n).
%p A322878 b:= proc(n, k, m, l) option remember; `if`(n<1, 1,
%p A322878      `if`(l-n>k, 0, b(n-1, k, m+1, n))+m*b(n-1, k, m, l))
%p A322878     end:
%p A322878 A:= (n, k)-> b(n-1, min(k, n-1), 1, n):
%p A322878 a:= n-> (k-> A(n, k)-A(n, k-1))(5):
%p A322878 seq(a(n), n=5..30);
%t A322878 b[n_, k_, m_, l_] := b[n, k, m, l] = If[n < 1, 1, If[l - n > k, 0, b[n - 1, k, m + 1, n]] + m b[n - 1, k, m, l]];
%t A322878 A[n_, k_] := b[n - 1, Min[k, n - 1], 1, n];
%t A322878 a[n_] := With[{k = 5}, A[n, k] - A[n, k - 1]];
%t A322878 a /@ Range[5, 30] (* _Jean-François Alcover_, May 05 2020, after Maple *)
%Y A322878 Column k=5 of A287215.
%Y A322878 Cf. A287254, A287255.
%K A322878 nonn
%O A322878 5,3
%A A322878 _Alois P. Heinz_, Dec 29 2018