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 A291130 Number of defective parking functions of length n and defect four. 2

%I #11 Feb 24 2019 02:00:36

%S 1,87,4320,176843,6768184,256059854,9846223168,390516805362,

%T 16102219296008,693122084961945,31208245366326896,1470819863019421317,

%U 72549461960461640120,3743176448672690767272,201836660477563528892704,11362223977488695430091444

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

%H Alois P. Heinz, <a href="/A291130/b291130.txt">Table of n, a(n) for n = 5..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) ~ (7*exp(1)/8 - 44*exp(2)/3 + 69*exp(3)/2 - 24*exp(4) + 5*exp(5)) * 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, 4)-S(n, 5):

%p seq(a(n), n=5..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, 4] - S[n, 5];

%t Table[a[n], {n, 5, 23}] (* _Jean-François Alcover_, Feb 24 2019, from Maple *)

%Y Column k=4 of A264902.

%K nonn

%O 5,2

%A _Alois P. Heinz_, Aug 18 2017

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Last modified June 23 10:25 EDT 2024. Contains 373629 sequences. (Running on oeis4.)