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A291136
Number of defective parking functions of length n and defect ten.
2
1, 4215, 2127828, 530926606, 92071525556, 12851428617547, 1561750852160556, 173226805226723844, 18081637592017744356, 1813499364725872444178, 177350996523515552397628, 17092810524840161845093436, 1636375630004710170560408532, 156537967540558397590739941650
OFFSET
11,2
LINKS
Peter J. Cameron, Daniel Johannsen, Thomas Prellberg, Pascal Schweitzer, Counting Defective Parking Functions, arXiv:0803.0302 [math.CO], 2008.
FORMULA
a(n) ~ (37*exp(1)/1209600 - 32*exp(2)/405 + 27459*exp(3)/4480 - 9728*exp(4)/105 + 71875*exp(5)/144 - 6264*exp(6)/5 + 13377*exp(7)/8 - 3776*exp(8)/3 + 1071*exp(9)/2 - 120*exp(10) + 11*exp(11)) * 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, 10)-S(n, 11):
seq(a(n), n=11..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, 10] - S[n, 11];
Table[a[n], {n, 11, 23}] (* Jean-François Alcover, Feb 24 2019, from Maple *)
CROSSREFS
Column k=10 of A264902.
Sequence in context: A229540 A250903 A250947 * A067140 A283725 A109488
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 18 2017
STATUS
approved