OFFSET
1,2
COMMENTS
For example, p=(4,1,2,5,3) has 2 circular successions: (1,2) and (3,4).
LINKS
S. M. Tanny, Permutations and successions, J. Combinatorial Theory, Series A, 21 (1976), 196-202.
FORMULA
a(n) = n*(n-1)*d(n-2), where d(j)=A000166(j) are the derangement numbers.
a(n) = A180188(n,1).
E.g.f.: x^2 * exp(-x) / (1 - x). - Ilya Gutkovskiy, Oct 11 2021
a(n) = 2 * A000387(n). - Alois P. Heinz, Oct 11 2021
D-finite with recurrence (-n+2)*a(n) +n*(n-3)*a(n-1) +n*(n-1)*a(n-2)=0. - R. J. Mathar, Jul 26 2022
EXAMPLE
a(4)=12 because we have 1*243, 142*3, 13*42, 31*24, 3142*, 431*2, 213*4, 4213*, 2*314, 2431*, 42*31, and 3*421 (the circular succession is marked *).
MAPLE
d[0] := 1: for n to 51 do d[n] := n*d[n-1]+(-1)^n end do: seq(n*(n-1)*d[n-2], n = 1 .. 22);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Sep 06 2010
STATUS
approved