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A261492 Number of partitions of subsets of {1,...,n}, where consecutive integers are required to be in the same part and the elements of {1, n} are required to be in the same part if they are both members of a subset.

%I A261492 #12 Feb 22 2017 09:50:23
%S A261492 1,2,4,8,18,42,102,254,648,1688,4486,12146,33474,93810,267112,772124,
%T A261492 2264214,6731254,20275118,61841886,190914356,596256556,1883148834,
%U A261492 6012081046,19395355770,63205986042,208003526516,691048272152,2317140259834,7839542054210
%N A261492 Number of partitions of subsets of {1,...,n}, where consecutive integers are required to be in the same part and the elements of {1, n} are required to be in the same part if they are both members of a subset.
%H A261492 Alois P. Heinz, <a href="/A261492/b261492.txt">Table of n, a(n) for n = 0..1000</a>
%F A261492 a(n) = 2 * Sum_{j=0..floor(n/2)} C(n,2*j) * A000110(j) for n>0, a(0) = 1.
%e A261492 a(3) = 8: {}, 1, 2, 3, 12, 23, 13, 123.
%e A261492 a(4) = 18: {}, 1, 2, 3, 4, 12, 13, 1|3, 14, 23, 24, 2|4, 34, 123, 124, 134, 234, 1234.
%p A261492 with(combinat):
%p A261492 a:= n-> `if`(n=0, 1, 2*add(binomial(n, 2*j)*bell(j), j=0..n/2)):
%p A261492 seq(a(n), n=0..35);
%t A261492 a[n_] := If[n==0, 1, 2*Sum[Binomial[n, 2*j]*BellB[j], {j, 0, n/2}]]; Table[ a[n], {n, 0, 35}] (* _Jean-François Alcover_, Feb 22 2017, translated from Maple *)
%Y A261492 Cf. A000110, A247100, A261134, A261041, A261489.
%K A261492 nonn
%O A261492 0,2
%A A261492 _Alois P. Heinz_, Aug 21 2015