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A261489 Number of partitions of subsets of {1,...,n}, where consecutive integers and the elements in {1, n} are required to be in different parts.

%I A261489 #11 Feb 02 2017 03:43:54
%S A261489 1,2,4,8,25,82,313,1318,6098,30603,165282,954065,5853242,37987146,
%T A261489 259751877,1864926846,14016442573,109985575616,898948324164,
%U A261489 7637000950875,67310106587314,614420757079213,5799709014601124,56530981389520624,568255134674637557
%N A261489 Number of partitions of subsets of {1,...,n}, where consecutive integers and the elements in {1, n} are required to be in different parts.
%H A261489 Alois P. Heinz, <a href="/A261489/b261489.txt">Table of n, a(n) for n = 0..250</a>
%e A261489 a(3) = 8: {}, 1, 2, 3, 1|2, 1|3, 2|3, 1|2|3.
%e A261489 a(4) = 25: {}, 1, 2, 3, 4, 1|2, 1|3, 13, 1|4, 2|3, 2|4, 24, 3|4, 1|2|3, 13|2, 1|2|4, 1|24, 1|3|4, 13|4, 2|3|4, 24|3, 1|2|3|4, 13|2|4, 1|3|24, 13|24.
%p A261489 g:= proc(n, l, t, f) option remember; `if`(n=0, 1,
%p A261489       add(`if`(l>0 and j=l or f=1 and n=1 and j=1, 0,
%p A261489       g(n-1, j, t+`if`(j=t, 1, 0), f)), j=0..t))
%p A261489     end:
%p A261489 a:= n-> `if`(n=0, 1, g(n-1, 0, 1, 0)+g(n-1, 1, 2, 1)):
%p A261489 seq(a(n), n=0..25);
%t A261489 g[n_, l_, t_, f_] := g[n, l, t, f] = If[n==0, 1, Sum[If[l>0 && j==l || f==1 && n==1 && j==1, 0, g[n-1, j, t+If[j==t, 1, 0], f]], {j, 0, t}]]; a[n_] := If[n==0, 1, g[n-1, 0, 1, 0]+g[n-1, 1, 2, 1]]; Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Feb 02 2017, translated from Maple *)
%Y A261489 Cf. A247100, A261134, A261041, A261492.
%K A261489 nonn
%O A261489 0,2
%A A261489 _Alois P. Heinz_, Aug 21 2015