cp's OEIS Frontend

A320557 Number of set partitions of [n] such that for each block b the smallest integer interval containing b has at most seven elements and for at least one block c the smallest integer interval containing c has exactly seven elements.

%I A320557 #6 Oct 17 2018 17:08:34
%S A320557 203,1197,4971,18223,63768,220419,779242,2845864,10418560,37768970,
%T A320557 135153976,477964329,1676343822,5852483376,20403590238,71080014610,
%U A320557 247360604490,859493636214,2980904955378,10318666659192,35656973487023,123042978647274,424121272321296
%N A320557 Number of set partitions of [n] such that for each block b the smallest integer interval containing b has at most seven elements and for at least one block c the smallest integer interval containing c has exactly seven elements.
%H A320557 Alois P. Heinz, <a href="/A320557/b320557.txt">Table of n, a(n) for n = 7..1000</a>
%F A320557 a(n) = A276723(n) - A276722(n).
%p A320557 b:= proc(n, m, l) option remember; `if`(n=0, 1,
%p A320557       add(b(n-1, max(m, j), [subsop(1=NULL, l)[],
%p A320557       `if`(j<=m, 0, j)]), j={l[], m+1} minus {0}))
%p A320557     end:
%p A320557 A:= (n, k)-> `if`(n=0, 1, `if`(k<2, k, b(n, 0, [0$(k-1)]))):
%p A320557 a:= n-> (k-> A(n, k) -`if`(k=0, 0, A(n, k-1)))(7):
%p A320557 seq(a(n), n=7..50);
%Y A320557 Column k=7 of A276727.
%Y A320557 Cf. A276722, A276723, A320620.
%K A320557 nonn,easy
%O A320557 7,1
%A A320557 _Alois P. Heinz_, Oct 15 2018