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A198434
Number of simple symmetric permutations of degree 2n (or 2n+1).
0
2, 10, 90, 966, 12338, 181470, 3018082, 55995486, 1146939010, 25716746430, 626755197698, 16502357651966, 466944932413442, 14133259249586174, 455715081098876418, 15596665064842012158, 564724372634695925762, 21568978799171323200510, 866674159679235417061378, 36548294282449538711357438
OFFSET
2,1
COMMENTS
A permutation is simple if the only intervals that are fixed are the singletons and [1..m].
A permutation p is symmetric if i+j=m+1 implies p(i)+p(j)=m+1.
For example the permutations
1234 and 12345
2413 25314
are both simple and symmetric.
Symmetric simple permutations of degree 2n+1 correspond to simple permutations in the Weyl group of type B_n.
Symmetric simple permutations of degree 2n correspond to simple permutations in the Weyl group of type C_n.
These occur in pairs so all entries in this sequence will be even.
LINKS
R. Dewji, I. Dimitrov, A. McCabe, M. Roth, D. Wehlau and J. Wilson,
EXAMPLE
The simple symmetric permutations of lowest degree are 2413, 3142, 25314, 41325.
CROSSREFS
Cf. A111111.
Sequence in context: A363425 A338050 A366268 * A326089 A377541 A277403
KEYWORD
nonn
AUTHOR
David Wehlau, Oct 24 2011
STATUS
approved