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A320560 Number of set partitions of [n] such that for each block b the smallest integer interval containing b has at most ten elements and for at least one block c the smallest integer interval containing c has exactly ten elements.

%I A320560 #7 Oct 17 2018 18:01:46
%S A320560 21147,172649,977607,4732307,21196160,91356135,387221998,1635077589,
%T A320560 6933701115,29953216031,132647186513,592562183163,2645622362009,
%U A320560 11748752847703,51794376799161,226629372792025,984996790932516,4257860514411454,18336632254191876
%N A320560 Number of set partitions of [n] such that for each block b the smallest integer interval containing b has at most ten elements and for at least one block c the smallest integer interval containing c has exactly ten elements.
%H A320560 Alois P. Heinz, <a href="/A320560/b320560.txt">Table of n, a(n) for n = 10..512</a>
%F A320560 a(n) = A276726(n) - A276725(n).
%p A320560 b:= proc(n, m, l) option remember; `if`(n=0, 1,
%p A320560       add(b(n-1, max(m, j), [subsop(1=NULL, l)[],
%p A320560       `if`(j<=m, 0, j)]), j={l[], m+1} minus {0}))
%p A320560     end:
%p A320560 A:= (n, k)-> `if`(n=0, 1, `if`(k<2, k, b(n, 0, [0$(k-1)]))):
%p A320560 a:= n-> (k-> A(n, k) -`if`(k=0, 0, A(n, k-1)))(10):
%p A320560 seq(a(n), n=10..40);
%Y A320560 Column k=10 of A276727.
%Y A320560 Cf. A276725, A276726, A320623.
%K A320560 nonn
%O A320560 10,1
%A A320560 _Alois P. Heinz_, Oct 15 2018