OFFSET
0,2
COMMENTS
a(n) counts endofunctions f:{1,...,2n}-> {1,...,2n} with f(f(i))=i for all i in {1,...,n}.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
EXAMPLE
a(1) = 3: (1,1), (1,2), (2,1).
MAPLE
g:= proc(n) g(n):= `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:
a:= n-> add(binomial(n, i)^2*i!*g(n-i)*(2*n)^(n-i), i=0..n):
seq(a(n), n=0..20);
MATHEMATICA
Join[{1}, Table[n! * Sum[Binomial[n, k] * 2^k * n^k* Sum[1/((k - 2*j)!*2^j*j!), {j, 0, Floor[k/2]}], {k, 0, n}], {n, 1, 20}]] (* Vaclav Kotesovec, Dec 05 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 21 2014
STATUS
approved