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A291130
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Number of defective parking functions of length n and defect four.
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2
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1, 87, 4320, 176843, 6768184, 256059854, 9846223168, 390516805362, 16102219296008, 693122084961945, 31208245366326896, 1470819863019421317, 72549461960461640120, 3743176448672690767272, 201836660477563528892704, 11362223977488695430091444
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OFFSET
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5,2
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LINKS
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FORMULA
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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
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MAPLE
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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, 4)-S(n, 5):
seq(a(n), n=5..23);
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MATHEMATICA
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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, 4] - S[n, 5];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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