%I #19 Nov 29 2018 16:18:03
%S 1,0,1,1,0,3,6,0,53,199,0,2908,13699,0,369985,2135430,0,87265700,
%T 611286653,0
%N Number of permutations of 3 indistinguishable copies of 1,...,n such that the first and second copies of j are adjacent and there are exactly j numbers between the second and the third copy of j.
%C a(n) = 0 for n == 1 (mod 3).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LangfordsProblem.html">Langford's Problem</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Dancing_Links">Dancing Links</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Langford_pairing">Langford pairing</a>
%e a(0) = 1: the empty permutation.
%e a(2) = 1: 221121.
%e a(3) = 1: 223321131.
%e a(5) = 3: 223325534411514, 225523344531141, 552244253341131.
%e a(6) = 6: 221121665544336543, 225523366534411614, 225526633544361141, 446611415563322532, 552266253344631141, 665544336543221121.
%Y Cf. A014552, A104185, A108235, A176127, A203435, A261516, A261517, A321956.
%K nonn,more
%O 0,6
%A _Alois P. Heinz_, Nov 25 2015