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A324352
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Total number of occurrences of 2 in the (signed) displacement sets of all permutations of [n+2] divided by 2!.
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3
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0, 1, 5, 28, 179, 1306, 10757, 98932, 1006007, 11214406, 136041329, 1784556808, 25174694723, 380087428618, 6115760751869, 104481070398556, 1888837397941487, 36026457717419662, 723015306101706857, 15230427461356523056, 336009169512596054459
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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)^3.
a(n) = -1/2! * Sum_{j=1..n} (-1)^j * binomial(n,j) * (n+2-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!)(2):
seq(a(n), n=0..23);
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MATHEMATICA
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m = 23;
CoefficientList[(1-Exp[-x])/(1-x)^3 + O[x]^(m+1), x]*Range[0, m]! (* Jean-François Alcover, May 03 2021 *)
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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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