A291128 Number of defective parking functions of length n and defect two.

1, 23, 436, 8402, 173860, 3924685, 96920092, 2612981360, 76612170196, 2432096760755, 83225580995116, 3056917610828590, 120045033150878404, 5021755110536666777, 223031850751250882620, 10484575680391970139980, 520227143451578652486196, 27175721567427682443046975

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

Column k=2 of A264902.

Sequence in context: A226847 A203147 A158453 * A174262 A174425 A076068

Adjacent sequences: A291125 A291126 A291127 * A291129 A291130 A291131

Keyword

nonn

Author

Alois P. Heinz, Aug 18 2017

Status

approved