OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..400
FORMULA
a(n) = [x^(2n)] (1-1/Sum_{j=0..2n} j!*x^j)^n.
a(n) is odd <=> n in { A131577 }.
a(n) ~ sqrt(2*Pi) * n^(n + 5/2) / exp(n-1). - Vaclav Kotesovec, Jun 25 2019
EXAMPLE
a(2) = 7: 1|342, 1|423, 1|432, 21|43, 231|4, 312|4, 321|4.
a(3) = 58: 1|2|4563, 1|2|4635, 1|2|4653, 1|2|5364, ..., 4213|5|6, 4231|5|6, 4312|5|6, 4321|5|6.
MATHEMATICA
p[n_] := p[n] = n! - Sum[k!*p[n - k], {k, 1, n - 1}];
(* T is A059438 *)
T[n_, k_] /; n < k = 0;
T[n_, 1] := p[n];
T[n_, k_] /; n >= k := T[n, k] = Sum[T[n - j, k - 1]*p[j], {j, 1, n}];
a[n_] := T[2n, n];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Aug 31 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 13 2019
STATUS
approved