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%I #10 Jul 18 2017 08:18:00
%S 1,1,3,13,75,541,4142,34792,322904,3303160,37046948,451109712,
%T 5923255272,83424945768,1254842021634,20081656282038,340747127912616,
%U 6111343349250912,115529870445001392,2296160998268520576,47869541875153872144,1044601509263870430000
%N Number of ordered set partitions of [n] such that for each block b the smallest integer interval containing b has at most five elements.
%H Alois P. Heinz, <a href="/A276895/b276895.txt">Table of n, a(n) for n = 0..449</a>
%F a(n) ~ exp(4) * n!. - _Vaclav Kotesovec_, Sep 22 2016
%t b[n_, m_, l_List] := b[n, m, l] = If[n == 0, m!, Sum[b[n - 1, Max[m, j], Append[ReplacePart[l, 1 -> Nothing], If[j <= m, 0, j]]], {j, Append[l, m + 1] ~Complement~ {0}}]]; a[n_] := b[n, 0, {0, 0, 0, 0}]; Table[a[n], {n, 0, 21}] (* _Jean-François Alcover_, Jul 18 2017, after _Alois P. Heinz_ *)
%Y Column k=5 of A276890.
%Y Cf. A276721.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Sep 21 2016