OFFSET
6,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 6..450
Wikipedia, Permutation
MAPLE
b:= proc(n, i, p) option remember; series(`if`(n=0 or i=1,
(p+n)!/n!*x^n, add(b(n-i*j, i-1, p+j)*(i-1)!^j*combinat
[multinomial](n, n-i*j, i$j)/j!^2*x^j, j=0..n/i)), x, 7)
end:
a:= n-> coeff(b(n$2, 0), x, 6):
seq(a(n), n=6..25);
MATHEMATICA
multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_, p_] := b[n, i, p] = Series[If[n == 0 || i == 1, (p + n)!/n!*x^n, Sum[b[n - i*j, i - 1, p + j]*(i - 1)!^j*multinomial[n, Join[{n - i*j}, Table[i, j]]]/j!^2*x^j, {j, 0, n/i}]], {x, 0, 7}];
a[n_] := Coefficient[b[n, n, 0], x, 6];
Table[a[n], {n, 6, 25}] (* Jean-François Alcover, May 30 2018, from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 27 2017
STATUS
approved