cp's OEIS Frontend

A350649 Number of partitions of [n] avoiding blocks containing their own index when blocks are ordered with decreasing largest elements.

%I A350649 #18 May 16 2022 04:58:41
%S A350649 1,0,1,1,6,16,73,298,1453,7366,40689,238258,1483306,9746839,67415262,
%T A350649 489048716,3710659737,29372630485,242021348787,2071598497189,
%U A350649 18386889241210,168944811545046,1604584556714162,15731291424746912,159001720653174800,1654891767547439393
%N A350649 Number of partitions of [n] avoiding blocks containing their own index when blocks are ordered with decreasing largest elements.
%H A350649 Alois P. Heinz, <a href="/A350649/b350649.txt">Table of n, a(n) for n = 0..576</a>
%H A350649 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%e A350649 a(4) = 6: 432|1, 42|31, 42|3|1, 4|31|2, 4|3|21, 4|3|2|1.
%p A350649 b:= proc(n, m) option remember; `if`(n=0, 1, add(
%p A350649       `if`(j=n, 0, b(n-1, max(m, j))), j=1..m+1))
%p A350649     end:
%p A350649 a:= n-> b(n, 0):
%p A350649 seq(a(n), n=0..25);
%t A350649 b[n_, m_] := b[n, m] = If[n == 0, 1, Sum[
%t A350649      If[j == n, 0, b[n-1, Max[m, j]]], {j, 1, m+1}]];
%t A350649 a[n_] := b[n, 0];
%t A350649 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, May 16 2022, after _Alois P. Heinz_ *)
%Y A350649 Column k=0 of A350647, A350684.
%K A350649 nonn
%O A350649 0,5
%A A350649 _Alois P. Heinz_, Jan 09 2022