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A324359
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Total number of occurrences of 9 in the (signed) displacement sets of all permutations of [n+9] divided by 9!.
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3
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0, 1, 19, 301, 4659, 73651, 1208849, 20736801, 372683159, 7020426511, 138543438429, 2861318625661, 61767341913539, 1391789835244251, 32689488282841529, 799220290375798681, 20312800343333343279, 535995638431063608871, 14665906835087251866389
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OFFSET
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0,3
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LINKS
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FORMULA
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E.g.f.: (1-exp(-x))/(1-x)^10.
a(n) = -1/9! * Sum_{j=1..n} (-1)^j * binomial(n,j) * (n+9-j)!.
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MAPLE
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a:= n-> (k-> -add((-1)^j*binomial(n, j)*(n+k-j)!, j=1..n)/k!)(9):
seq(a(n), n=0..23);
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MATHEMATICA
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Range[0, 20]! CoefficientList[Series[(1 - Exp[-x])/(1 - x)^10, {x, 0, 20}], x] (* Vincenzo Librandi, Jun 06 2019 *)
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PROG
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(Magma) [0] cat [(-1/Factorial(9)) * &+[(-1)^j * Binomial(n, j) * Factorial(n+9-j) : j in [1..n]]: n in [1..20]]; // Vincenzo Librandi, Jun 06 2019
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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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