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A291136
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Number of defective parking functions of length n and defect ten.
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2
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1, 4215, 2127828, 530926606, 92071525556, 12851428617547, 1561750852160556, 173226805226723844, 18081637592017744356, 1813499364725872444178, 177350996523515552397628, 17092810524840161845093436, 1636375630004710170560408532, 156537967540558397590739941650
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OFFSET
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11,2
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LINKS
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FORMULA
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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
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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, 10)-S(n, 11):
seq(a(n), n=11..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, 10] - S[n, 11];
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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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