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A184177 Number of set partitions of {1,2,...,n} having no blocks of the form {i,i+1,i+2}.

%I A184177 #10 Jul 27 2019 21:51:34
%S A184177 1,1,2,4,13,46,184,805,3840,19775,109180,642382,4007712,26399764,
%T A184177 182939900,1329327991,10100670183,80053631844,660328296777,
%U A184177 5657449573120,50255253534312,462096537041953,4391648990609487,43079839534282880
%N A184177 Number of set partitions of {1,2,...,n} having no blocks of the form {i,i+1,i+2}.
%C A184177 a(n) = A184176(n,0).
%F A184177 a(n) = Sum_{j=0..floor(n/3)} (-1)^j * binomial(n-2j,j) * Bell(n-3j,j).
%e A184177 a(3) = 4 because we have 1-2-3, 1-23, 12-3, and 13-2.
%e A184177 a(4) = 13 because among the 15 (= Bell(4)) partitions of {1,2,3,4} only 123-4 and 1-234 have adjacent blocks of size 3.
%p A184177 with(combinat): seq(add((-1)^j*binomial(n-2*j, j)*bell(n-3*j), j = 0 .. floor((1/3)*n)), n = 0 .. 23);
%Y A184177 Cf. A184176, A124323, A000296, A184174, A184175.
%K A184177 nonn
%O A184177 0,3
%A A184177 _Emeric Deutsch_, Feb 09 2011