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A078480
Number of permutations p of {1,2,...,n} such that |p(i)-i| != 1 for all i.
5
1, 1, 1, 2, 5, 21, 117, 792, 6205, 55005, 543597, 5922930, 70518905, 910711193, 12678337945, 189252400480, 3015217932073, 51067619064873, 916176426422089, 17355904144773970, 346195850534379613, 7252654441500887309
OFFSET
0,4
COMMENTS
For positive n, a(n) equals the permanent of the n X n matrix with 0's along the superdiagonal and the subdiagonal, and 1's everywhere else. [John M. Campbell, Jul 09 2011]
LINKS
V. Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 223.
N. S. Mendelsohn, The asymptotic series for a certain class of permutation problems, Canadian Journal of Mathematics, vol. VIII, No.2, 1956, p.238 (Example 5).
FORMULA
G.f.: 1/(1-x^2)*Sum_{n>=0} n!*(x/(1+x)^2)^n. - Vladeta Jovovic, Jun 26 2007
Asymptotic (N. S. Mendelsohn, 1956): a(n)/n! -> 1/e^2
Recurrence: a(n) = n*a(n-1) - (n-2)*a(n-3) - a(n-4), for n>=5
MATHEMATICA
(* Explicit formula: *) Table[Sum[Sum[(-1)^k*(i-k)!*Binomial[2i-k, k], {k, 0, i}], {i, 0, n}], {n, 0, 21}] (* Vaclav Kotesovec, Mar 28 2011 *)
CROSSREFS
Column k=0 of A320582.
Column k=1 of A306512.
Sequence in context: A129582 A152576 A328286 * A212922 A243272 A139153
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Jan 03 2003
STATUS
approved