A291129 Number of defective parking functions of length n and defect three.

1, 46, 1442, 41070, 1166083, 34268902, 1059688652, 34723442062, 1208687001381, 44701813604150, 1754724115372438, 72987949807322222, 3210789166789472775, 149073947870611952326, 7289995971215959818304, 374726414201304528649678, 20207920615298454956444905

Offset

4,2

Links

Alois P. Heinz, Table of n, a(n) for n = 4..387

Peter J. Cameron, Daniel Johannsen, Thomas Prellberg, Pascal Schweitzer, Counting Defective Parking Functions, arXiv:0803.0302 [math.CO], 2008.

Formula

a(n) ~ (-13*exp(1)/6 + 14*exp(2) - 15*exp(3) + 4*exp(4)) * 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, 3)-S(n, 4):
seq(a(n), n=4..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, 3] - S[n, 4];
Table[a[n], {n, 4, 23}] (* Jean-François Alcover, Feb 24 2019, from Maple *)

Crossrefs

Column k=3 of A264902.

Sequence in context: A332858 A264505 A308101 * A115608 A318044 A263190

Adjacent sequences: A291126 A291127 A291128 * A291130 A291131 A291132

Keyword

nonn

Author

Alois P. Heinz, Aug 18 2017

Status

approved