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Number of ordered set partitions of [n] such that for each block b the smallest integer interval containing b has at most three elements.
3

%I #10 Jul 18 2017 08:17:30

%S 1,1,3,13,62,352,2348,17880,153138,1458726,15303672,175387056,

%T 2180632824,29240091480,420683340840,6464876260440,105699125013120,

%U 1832140771795440,33562515077608320,647929998101403360,13148236101412979280,279809650659550924080

%N Number of ordered set partitions of [n] such that for each block b the smallest integer interval containing b has at most three elements.

%H Alois P. Heinz, <a href="/A276893/b276893.txt">Table of n, a(n) for n = 0..449</a>

%F a(n) ~ exp(2) * 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}]; Table[a[n], {n, 0, 21}] (* _Jean-François Alcover_, Jul 18 2017, after _Alois P. Heinz_ *)

%Y Column k=3 of A276890.

%Y Cf. A129847.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Sep 21 2016