cp's OEIS Frontend

A287668 Number of set partitions of [n] such that j is member of block b only if b = 1 or at least one of j-1, ..., j-5 is member of a block >= b-1.

%I A287668 #9 Dec 11 2020 13:38:59
%S A287668 1,1,2,5,15,52,203,877,4139,21107,115301,670059,4119316,26665103,
%T A287668 181031235,1284643851,9500643629,73037739470,582346938182,
%U A287668 4805997066022,40980051074202,360452146946076,3265691382361850,30435437254066599,291431082211368120
%N A287668 Number of set partitions of [n] such that j is member of block b only if b = 1 or at least one of j-1, ..., j-5 is member of a block >= b-1.
%H A287668 Alois P. Heinz, <a href="/A287668/b287668.txt">Table of n, a(n) for n = 0..55</a>
%F A287668 a(n) = A287641(n,5).
%F A287668 a(n) = A000110(n) for n <= 7.
%e A287668 a(8) = 4139 = 4140 - 1 = A000110(8) - 1 counts all set partitions of [8] except: 134567|2|8.
%p A287668 b:= proc(n, l) option remember; `if`(n=0, 1, add(b(n-1,
%p A287668       [seq(max(l[i], j), i=2..nops(l)), j]), j=1..l[1]+1))
%p A287668     end:
%p A287668 a:= n-> b(n, [0$5]):
%p A287668 seq(a(n), n=0..24);
%t A287668 b[n_, l_] := b[n, l] = If[n == 0, 1, Sum[b[n - 1, Append[Table[Max[l[[i]], j], {i, 2, Length[l]}], j]], {j, 1, l[[1]] + 1}]];
%t A287668 a[n_] := b[n, Table[0, {5}]];
%t A287668 a /@ Range[0, 24] (* _Jean-François Alcover_, Dec 11 2020, after _Alois P. Heinz_ *)
%Y A287668 Column k=5 of A287641.
%Y A287668 Cf. A000110.
%K A287668 nonn
%O A287668 0,3
%A A287668 _Alois P. Heinz_, May 29 2017