A324355 Total number of occurrences of 5 in the (signed) displacement sets of all permutations of [n+5] divided by 5!.

0, 1, 11, 109, 1115, 12151, 142205, 1788361, 24118967, 347811859, 5345895929, 87298986325, 1510075068419, 27590646911023, 531082929791861, 10743610293871681, 227906995674679535, 5059315590877577131, 117308151182930808977, 2835988521500605314829

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..445

Wikipedia, Permutation

Formula

E.g.f.: (1-exp(-x))/(1-x)^6.

a(n) = -1/5! * Sum_{j=1..n} (-1)^j * binomial(n,j) * (n+5-j)!.

a(n) = A306234(n+5,5).

Maple

a:= n-> (k-> -add((-1)^j*binomial(n, j)*(n+k-j)!, j=1..n)/k!)(5):
seq(a(n), n=0..23);

Mathematica

m = 23;
CoefficientList[(1-Exp[-x])/(1-x)^6 + O[x]^(m+1), x]*Range[0, m]! (* Jean-François Alcover, May 03 2021 *)

Crossrefs

Column k=5 of A324362.

Cf. A306234.

Sequence in context: A287836 A124290 A094703 * A331537 A169631 A308005

Adjacent sequences: A324352 A324353 A324354 * A324356 A324357 A324358

Keyword

nonn

Author

Alois P. Heinz, Feb 23 2019

Status

approved