cp's OEIS Frontend

A224986 a(n) = Product_{k=1..n-4} (n-k-2)!^(k*k!).

%I A224986 #15 Aug 06 2020 22:11:49
%S A224986 1,1,1,1,2,96,8153726976,
%T A224986 320352637207127391364950814323398779319161580421120
%N A224986 a(n) = Product_{k=1..n-4} (n-k-2)!^(k*k!).
%C A224986 Consider words on n symbols that contain every permutation of those n symbols as contiguous substrings. The minimal length of such a string was conjectured to equal A007489(n) (see A180632). This sequence is a lower bound on the number of distinct (up to relabeling the symbols) such strings of the conjectured minimal length.
%C A224986 It was conjectured in the Ashlock paper that, for all n, there is only one string of length A007489(n) containing all permutations. This sequence shows that this conjecture fails as n grows.
%C A224986 In 2014 Houston has shown that the first conjecture about the minimal length is also false for all n > 5. In particular, A180632(6) <= 872 = A007489(n). - _M. F. Hasler_, Jul 28 2020
%C A224986 The next term a(9) ~ 2.18e291 is too large to be displayed here. - _M. F. Hasler_, Jul 29 2020
%D A224986 D. Ashlock and J. Tillotson, Construction of small superpermutations and minimal injective superstrings. Congressus Numerantium, 93 (1993), 91-98.
%H A224986 Robin Houston, <a href="http://arxiv.org/abs/1408.5108">Tackling the Minimal Superpermutation Problem</a>, arXiv:1408.5108 [math.CO], 2014.
%H A224986 Nathaniel Johnston, <a href="http://arxiv.org/abs/1303.4150">Non-uniqueness of minimal superpermutations</a>, arXiv:1303.4150 [math.CO], 2013; Discrete Math., 313 (2013), 1553-1557.
%H A224986 Nathaniel Johnston, <a href="http://www.njohnston.ca/2013/04/the-minimal-superpermutation-problem/">The Minimal Superpermutation Problem</a>, 2013.
%e A224986 a(n) = 1 for n <= 4, which agrees with the fact that the minimal strings containing all permutations in these cases are unique (see A180632).
%p A224986 seq(product((n-k-2)!^(k*k!),k=1..max(n-4,0)),n=1..8);
%o A224986 (PARI) apply( {A224986(n)=prod(k=1,n-4,(n-k-2)!^(k*k!))}, [1..8]) \\ _M. F. Hasler_, Jul 29 2020
%Y A224986 Cf. A180632, A188428.
%K A224986 nonn,easy
%O A224986 1,5
%A A224986 _Nathaniel Johnston_, Apr 22 2013