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A324359 Total number of occurrences of 9 in the (signed) displacement sets of all permutations of [n+9] divided by 9!. 3
0, 1, 19, 301, 4659, 73651, 1208849, 20736801, 372683159, 7020426511, 138543438429, 2861318625661, 61767341913539, 1391789835244251, 32689488282841529, 799220290375798681, 20312800343333343279, 535995638431063608871, 14665906835087251866389 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Wikipedia, Permutation
FORMULA
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)!.
a(n) = A306234(n+9,9).
MAPLE
a:= n-> (k-> -add((-1)^j*binomial(n, j)*(n+k-j)!, j=1..n)/k!)(9):
seq(a(n), n=0..23);
MATHEMATICA
Range[0, 20]! CoefficientList[Series[(1 - Exp[-x])/(1 - x)^10, {x, 0, 20}], x] (* Vincenzo Librandi, Jun 06 2019 *)
PROG
(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
CROSSREFS
Column k=9 of A324362.
Cf. A306234.
Sequence in context: A152591 A051562 A330846 * A074460 A267010 A182460
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 23 2019
STATUS
approved

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Last modified March 29 08:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)