OFFSET
0,3
COMMENTS
a(n) is also the number of endofunctions on [2n] such that n is the range maximum and the number of elements that are mapped to m is divisible by m. a(2) = 7: (2211), (2121), (2112), (1221), (1212), (1122), (2222).
All terms are odd.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..503
FORMULA
a(n) = A364285(2n,n).
EXAMPLE
a(2) = 7: 2ab11cd, 2ac11bd, 2ad11bc, 2bc11ad, 2bd11ac, 2cd11ab, 22abcd.
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(b(n-i*j, i-1)*binomial(n, i*j), j=0..n/i)))
end:
a:= n-> b(2*n, n)-`if`(n=0, 0, b(2*n, n-1)):
seq(a(n), n=0..23);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 18 2023
STATUS
approved