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A322875 Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals two.

%I A322875 #11 Dec 14 2020 07:52:24
%S A322875 0,1,5,21,86,361,1584,7315,35635,183080,990659,5635021,33622161,
%T A322875 209973099,1369560267,9310957518,65852852210,483672626464,
%U A322875 3683088047043,29033382412670,236591717703447,1990467019391404,17268021545339042,154304401318961489
%N A322875 Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals two.
%H A322875 Alois P. Heinz, <a href="/A322875/b322875.txt">Table of n, a(n) for n = 2..590</a>
%H A322875 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A322875 a(n) = A287252(n) - A026898(n-1).
%p A322875 b:= proc(n, k, m, l) option remember; `if`(n<1, 1,
%p A322875      `if`(l-n>k, 0, b(n-1, k, m+1, n))+m*b(n-1, k, m, l))
%p A322875     end:
%p A322875 A:= (n, k)-> b(n-1, min(k, n-1), 1, n):
%p A322875 a:= n-> (k-> A(n, k)-A(n, k-1))(2):
%p A322875 seq(a(n), n=2..30);
%t A322875 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 A322875 A[n_, k_] := b[n - 1, Min[k, n - 1], 1, n];
%t A322875 a[n_] := With[{k = 2}, A[n, k] - A[n, k - 1]];
%t A322875 a /@ Range[2, 30] (* _Jean-François Alcover_, Dec 14 2020, after _Alois P. Heinz_ *)
%Y A322875 Column k=2 of A287215.
%Y A322875 Cf. A026898, A287252.
%K A322875 nonn
%O A322875 2,3
%A A322875 _Alois P. Heinz_, Dec 29 2018