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A291131

Number of defective parking functions of length n and defect five.

1, 162, 12357, 710314, 36046214, 1735513330, 82324649310, 3930328083098, 191251911975191, 9558232936557458, 492897541966818651, 26298973648144245066, 1454100613639405907108, 83377530695619365120818, 4959049035365905488761452, 305903708967397161238879674

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OFFSET

6,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 6..386

Peter J. Cameron, Daniel Johannsen, Thomas Prellberg, Pascal Schweitzer, Counting Defective Parking Functions, arXiv:0803.0302 [math.CO], 2008.

FORMULA

a(n) ~ (-31*exp(1)/120 + 32*exp(2)/3 - 99*exp(3)/2 + 68*exp(4) - 35*exp(5) + 6*exp(6)) * 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, 5)-S(n, 6):

seq(a(n), n=6..23);