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A291134
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Number of defective parking functions of length n and defect eight.
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2
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1, 1103, 269512, 38643849, 4218834608, 393933602129, 33499946915016, 2693983725947891, 209859823775671984, 16093162912317174422, 1228462028909579534968, 94081283153407041089350, 7269699339591280955315232, 569088494101518607733459806
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OFFSET
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9,2
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LINKS
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FORMULA
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a(n) ~ (73*exp(1)/40320 - 296*exp(2)/315 + 405*exp(3)/16 - 2432*exp(4)/15 + 9625*exp(5)/24 - 468*exp(6) + 553*exp(7)/2 - 80*exp(8) + 9*exp(9)) * 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, 8)-S(n, 9):
seq(a(n), n=9..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, 8] - S[n, 9];
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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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