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

%I A291128 #11 Aug 20 2018 11:27:40
%S A291128 1,23,436,8402,173860,3924685,96920092,2612981360,76612170196,
%T A291128 2432096760755,83225580995116,3056917610828590,120045033150878404,
%U A291128 5021755110536666777,223031850751250882620,10484575680391970139980,520227143451578652486196,27175721567427682443046975
%N A291128 Number of defective parking functions of length n and defect two.
%H A291128 Alois P. Heinz, <a href="/A291128/b291128.txt">Table of n, a(n) for n = 3..387</a>
%H A291128 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 A291128 a(n) ~ (7*exp(1)/2 - 8*exp(2) + 3*exp(3)) * n^(n-1). - _Vaclav Kotesovec_, Aug 19 2017
%p A291128 S:= (n, k)-> add(binomial(n, i)*k*(k+i)^(i-1)*(n-k-i)^(n-i), i=0..n-k):
%p A291128 a:= n-> S(n, 2)-S(n, 3):
%p A291128 seq(a(n), n=3..23);
%t A291128 S[n_, k_] := Sum[Binomial[n, i]*k*(k+i)^(i-1)*(n-k-i)^(n-i), {i, 0, n-k}];
%t A291128 a[n_] := S[n, 2] - S[n, 3];
%t A291128 Table[a[n], {n, 3, 23}] (* _Jean-François Alcover_, Aug 20 2018, from Maple *)
%Y A291128 Column k=2 of A264902.
%K A291128 nonn
%O A291128 3,2
%A A291128 _Alois P. Heinz_, Aug 18 2017