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A322882 Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals nine.

%I A322882 #5 Dec 29 2018 16:48:55
%S A322882 0,1,259,7851,123693,1517480,16628928,172861375,1757583339,
%T A322882 17780116911,180778826049,1858914009077,19407229306905,
%U A322882 206203531592425,2232778235440364,24655217395787251,277719538910592762,3191229583066629810,37404691679158439649
%N A322882 Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals nine.
%H A322882 Alois P. Heinz, <a href="/A322882/b322882.txt">Table of n, a(n) for n = 9..579</a>
%H A322882 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A322882 a(n) = A287259(n) - A287258(n).
%p A322882 b:= proc(n, k, m, l) option remember; `if`(n<1, 1,
%p A322882      `if`(l-n>k, 0, b(n-1, k, m+1, n))+m*b(n-1, k, m, l))
%p A322882     end:
%p A322882 A:= (n, k)-> b(n-1, min(k, n-1), 1, n):
%p A322882 a:= n-> (k-> A(n, k)-A(n, k-1))(9):
%p A322882 seq(a(n), n=9..30);
%Y A322882 Column k=9 of A287215.
%Y A322882 Cf. A287258, A287259.
%K A322882 nonn
%O A322882 9,3
%A A322882 _Alois P. Heinz_, Dec 29 2018