A322882 - OEIS

%I #5 Dec 29 2018 16:48:55

%S 0,1,259,7851,123693,1517480,16628928,172861375,1757583339,

%T 17780116911,180778826049,1858914009077,19407229306905,

%U 206203531592425,2232778235440364,24655217395787251,277719538910592762,3191229583066629810,37404691679158439649

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

%H Alois P. Heinz, <a href="/A322882/b322882.txt">Table of n, a(n) for n = 9..579</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

%F a(n) = A287259(n) - A287258(n).

%p b:= proc(n, k, m, l) option remember; `if`(n<1, 1,

%p      `if`(l-n>k, 0, b(n-1, k, m+1, n))+m*b(n-1, k, m, l))

%p     end:

%p A:= (n, k)-> b(n-1, min(k, n-1), 1, n):

%p a:= n-> (k-> A(n, k)-A(n, k-1))(9):

%p seq(a(n), n=9..30);

%Y Column k=9 of A287215.

%Y Cf. A287258, A287259.

%K nonn

%O 9,3

%A _Alois P. Heinz_, Dec 29 2018