cp's OEIS Frontend

A287666 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-3 is member of a block >= b-1.

%I A287666 #12 May 27 2018 10:32:54
%S A287666 1,1,2,5,15,52,202,861,3970,19596,102703,567867,3295439,19986462,
%T A287666 126231946,827759525,5621051650,39439867696,285368007479,
%U A287666 2125566382124,16273261632111,127881070062521,1030221084660031,8498826714433335,71721238761675612,618573094313147709
%N A287666 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-3 is member of a block >= b-1.
%H A287666 Alois P. Heinz, <a href="/A287666/b287666.txt">Table of n, a(n) for n = 0..150</a>
%H A287666 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A287666 a(n) = A287641(n,3).
%F A287666 a(n) = A000110(n) for n <= 5.
%e A287666 a(6) = 202 = 203 - 1 = A000110(6) - 1 counts all set partitions of [6] except: 1345|2|6.
%p A287666 b:= proc(n, l) option remember; `if`(n=0, 1, add(b(n-1,
%p A287666       [seq(max(l[i], j), i=2..nops(l)), j]), j=1..l[1]+1))
%p A287666     end:
%p A287666 a:= n-> b(n, [0$3]):
%p A287666 seq(a(n), n=0..26);
%t A287666 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 A287666 a[n_] := b[n, {0, 0, 0}];
%t A287666 Table[a[n], {n, 0, 26}] (* _Jean-François Alcover_, May 27 2018, from Maple *)
%Y A287666 Column k=3 of A287641.
%Y A287666 Cf. A000110.
%K A287666 nonn
%O A287666 0,3
%A A287666 _Alois P. Heinz_, May 29 2017