A291135 - OEIS

%I #12 Feb 24 2019 08:42:01

%S 1,2146,754943,143336610,19795924787,2267392009178,231141766226605,

%T 21881366451890002,1976997422623843358,173666031731576614842,

%U 15025473411620865716938,1292364106829281911023554,111260031164008673095102874,9635674549219284395173044506

%N Number of defective parking functions of length n and defect nine.

%H Alois P. Heinz, <a href="/A291135/b291135.txt">Table of n, a(n) for n = 10..386</a>

%H Peter J. Cameron, Daniel Johannsen, Thomas Prellberg, Pascal Schweitzer, <a href="https://arxiv.org/abs/0803.0302">Counting Defective Parking Functions</a>, arXiv:0803.0302 [math.CO], 2008.

%F a(n) ~ (-13*exp(1)/51840 + 92*exp(2)/315 - 7533*exp(3)/560 + 6016*exp(4)/45 - 11875*exp(5)/24 + 864*exp(6) - 4753*exp(7)/6 + 392*exp(8) - 99*exp(9) + 10*exp(10)) * n^(n-1). - _Vaclav Kotesovec_, Aug 19 2017

%p S:= (n, k)-> add(binomial(n, i)*k*(k+i)^(i-1)*(n-k-i)^(n-i), i=0..n-k):

%p a:= n-> S(n, 9)-S(n, 10):

%p seq(a(n), n=10..23);

%t S[n_, k_] := Sum[Binomial[n, i]*k*(k+i)^(i-1)*(n-k-i)^(n-i), {i, 0, n-k}];

%t a[n_] := S[n, 9] - S[n, 10];

%t Table[a[n], {n, 10, 23}] (* _Jean-François Alcover_, Feb 24 2019, from Maple *)

%Y Column k=9 of A264902.

%K nonn

%O 10,2

%A _Alois P. Heinz_, Aug 18 2017