A291132 Number of defective parking functions of length n and defect six.

1, 303, 34660, 2743112, 181875244, 11023248678, 639875755364, 36555471741284, 2090131479753756, 120898503338385149, 7124218746544184628, 429662666436736162636, 26601747798152634836236, 1694092238645618305809580, 111106187207006959809867012

Offset: 7

Author

Alois P. Heinz, Aug 18 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..386
• Peter J. Cameron, Daniel Johannsen, Thomas Prellberg, Pascal Schweitzer, Counting Defective Parking Functions, arXiv:0803.0302 [math.CO], 2008.

Crossrefs

Column k=6 of A264902.

Programs

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, 6)-S(n, 7):
seq(a(n), n=7..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, 6] - S[n, 7];
Table[a[n], {n, 7, 23}] (* Jean-François Alcover, Feb 24 2019, from Maple *)

Formula

a(n) ~ (43*exp(1)/720 - 88*exp(2)/15 + 405*exp(3)/8 - 368*exp(4)/3 + 235*exp(5)/2 - 48*exp(6) + 7*exp(7)) * n^(n-1). - Vaclav Kotesovec, Aug 19 2017