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A320558 Number of set partitions of [n] such that for each block b the smallest integer interval containing b has at most eight elements and for at least one block c the smallest integer interval containing c has exactly eight elements.

%I A320558 #6 Oct 17 2018 17:31:50
%S A320558 877,5852,27267,110545,422396,1578192,5877165,22355618,87597223,
%T A320558 345223398,1352883364,5249340393,20158426185,76729396494,290259302392,
%U A320558 1094289866107,4121529511428,15518374075986,58402401729381,219602989556557,824720185307142,3092742982300231
%N A320558 Number of set partitions of [n] such that for each block b the smallest integer interval containing b has at most eight elements and for at least one block c the smallest integer interval containing c has exactly eight elements.
%H A320558 Alois P. Heinz, <a href="/A320558/b320558.txt">Table of n, a(n) for n = 8..1000</a>
%F A320558 a(n) = A276724(n) - A276723(n).
%p A320558 b:= proc(n, m, l) option remember; `if`(n=0, 1,
%p A320558       add(b(n-1, max(m, j), [subsop(1=NULL, l)[],
%p A320558       `if`(j<=m, 0, j)]), j={l[], m+1} minus {0}))
%p A320558     end:
%p A320558 A:= (n, k)-> `if`(n=0, 1, `if`(k<2, k, b(n, 0, [0$(k-1)]))):
%p A320558 a:= n-> (k-> A(n, k) -`if`(k=0, 0, A(n, k-1)))(8):
%p A320558 seq(a(n), n=8..50);
%Y A320558 Column k=8 of A276727.
%Y A320558 Cf. A276723, A276724, A320621.
%K A320558 nonn,easy
%O A320558 8,1
%A A320558 _Alois P. Heinz_, Oct 15 2018