%I #9 Dec 08 2020 08:37:17

%S 15,64,201,585,1741,5375,16355,48601,141921,410425,1182828,3398411,

%T 9728692,27745449,78861484,223573925,632578393,1786856056,5039984789,

%U 14197033194,39945491361,112282665839,315352029653,885048266680,2482371076351,6958712870273

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

%H Alois P. Heinz, <a href="/A320555/b320555.txt">Table of n, a(n) for n = 5..1000</a>

%F a(n) = A276721(n) - A276720(n).

%p b:= proc(n, m, l) option remember; `if`(n=0, 1,

%p add(b(n-1, max(m, j), [subsop(1=NULL, l)[],

%p `if`(j<=m, 0, j)]), j={l[], m+1} minus {0}))

%p end:

%p A:= (n, k)-> `if`(n=0, 1, `if`(k<2, k, b(n, 0, [0$(k-1)]))):

%p a:= n-> (k-> A(n, k) -`if`(k=0, 0, A(n, k-1)))(5):

%p seq(a(n), n=5..50);

%t b[n_, m_, l_List] := b[n, m, l] = If[n == 0, 1, Sum[b[n - 1, Max[m, j], Append[ReplacePart[l, 1 -> Nothing], If[j <= m, 0, j]]], {j, Append[l, m + 1]~Complement~{0}}]];

%t A[n_, k_] := If[n == 0, 1, If[k < 2, k, b[n, 0, Array[0 &, k - 1]]]];

%t a[n_] := With[{k = 5}, A[n, k] - If[k == 0, 0, A[n, k - 1]]];

%t a /@ Range[5, 35] (* _Jean-François Alcover_, Dec 08 2020, after _Alois P. Heinz_ *)

%Y Column k=5 of A276727.

%Y Cf. A276720, A276721, A320618.

%K nonn,easy

%O 5,1

%A _Alois P. Heinz_, Oct 15 2018