OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..450
Wikipedia, Permutation
EXAMPLE
a(3) = 4: (123), (132), (13)(2), (1)(23).
a(4) = 10: (1234), (1243), (1324), (1342), (1423), (1432), (124)(3),
(142)(3), (1)(234), (1)(243).
MAPLE
a:= proc(m) option remember; local b; b:=
proc(n, i, p) option remember; `if`(i*(i+1)/2<n, 0,
`if`(n=0, p!*(m-p)!, b(n, i-1, p)+b(n-i, min(n-i, i-1), p-1)))
end: b(m$3)
end:
seq(a(n), n=0..24);
MATHEMATICA
a[m_] := a[m] = Module[{b}, b[n_, i_, p_] := b[n, i, p] = If[i(i+1)/2 < n, 0, If[n == 0, p!*(m - p)!, b[n, i - 1, p] + b[n - i, Min[n - i, i - 1], p - 1]]]; b[m, m, m]];
Table[a[n], {n, 0, 24}] (* Jean-François Alcover, Oct 21 2023, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 17 2023
STATUS
approved