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A320559 Number of set partitions of [n] such that for each block b the smallest integer interval containing b has at most nine elements and for at least one block c the smallest integer interval containing c has exactly nine elements.

%I A320559 #7 Oct 17 2018 17:59:41
%S A320559 4140,30751,158766,705926,2928164,11774145,46852653,186723275,
%T A320559 759062433,3170429794,13343960839,56013146481,233387096649,
%U A320559 963938933894,3948441860748,16062919807404,65036845178255,262641546675463,1059920408695467,4277149345637299
%N A320559 Number of set partitions of [n] such that for each block b the smallest integer interval containing b has at most nine elements and for at least one block c the smallest integer interval containing c has exactly nine elements.
%H A320559 Alois P. Heinz, <a href="/A320559/b320559.txt">Table of n, a(n) for n = 9..512</a>
%F A320559 a(n) = A276725(n) - A276724(n).
%p A320559 b:= proc(n, m, l) option remember; `if`(n=0, 1,
%p A320559       add(b(n-1, max(m, j), [subsop(1=NULL, l)[],
%p A320559       `if`(j<=m, 0, j)]), j={l[], m+1} minus {0}))
%p A320559     end:
%p A320559 A:= (n, k)-> `if`(n=0, 1, `if`(k<2, k, b(n, 0, [0$(k-1)]))):
%p A320559 a:= n-> (k-> A(n, k) -`if`(k=0, 0, A(n, k-1)))(9):
%p A320559 seq(a(n), n=9..40);
%Y A320559 Column k=9 of A276727.
%Y A320559 Cf. A276724, A276725, A320622.
%K A320559 nonn
%O A320559 9,1
%A A320559 _Alois P. Heinz_, Oct 15 2018