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A324352
Total number of occurrences of 2 in the (signed) displacement sets of all permutations of [n+2] divided by 2!.
3
0, 1, 5, 28, 179, 1306, 10757, 98932, 1006007, 11214406, 136041329, 1784556808, 25174694723, 380087428618, 6115760751869, 104481070398556, 1888837397941487, 36026457717419662, 723015306101706857, 15230427461356523056, 336009169512596054459
OFFSET
0,3
LINKS
Wikipedia, Permutation
FORMULA
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)!.
a(n) = A306234(n+2,2).
MAPLE
a:= n-> (k-> -add((-1)^j*binomial(n, j)*(n+k-j)!, j=1..n)/k!)(2):
seq(a(n), n=0..23);
MATHEMATICA
m = 23;
CoefficientList[(1-Exp[-x])/(1-x)^3 + O[x]^(m+1), x]*Range[0, m]! (* Jean-François Alcover, May 03 2021 *)
CROSSREFS
Column k=2 of A324362.
Cf. A306234.
Sequence in context: A082031 A020081 A095676 * A006157 A179326 A156629
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 23 2019
STATUS
approved