OFFSET
3,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 3..387
Peter J. Cameron, Daniel Johannsen, Thomas Prellberg, Pascal Schweitzer, Counting Defective Parking Functions, arXiv:0803.0302 [math.CO], 2008
FORMULA
a(n) ~ (7*exp(1)/2 - 8*exp(2) + 3*exp(3)) * n^(n-1). - Vaclav Kotesovec, Aug 19 2017
MAPLE
S:= (n, k)-> add(binomial(n, i)*k*(k+i)^(i-1)*(n-k-i)^(n-i), i=0..n-k):
a:= n-> S(n, 2)-S(n, 3):
seq(a(n), n=3..23);
MATHEMATICA
S[n_, k_] := Sum[Binomial[n, i]*k*(k+i)^(i-1)*(n-k-i)^(n-i), {i, 0, n-k}];
a[n_] := S[n, 2] - S[n, 3];
Table[a[n], {n, 3, 23}] (* Jean-François Alcover, Aug 20 2018, from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 18 2017
STATUS
approved