A324356 Total number of occurrences of 6 in the (signed) displacement sets of all permutations of [n+6] divided by 6!.

0, 1, 13, 148, 1707, 20686, 266321, 3652608, 53339831, 827870338, 13624599309, 237169578724, 4356110013107, 84220077081414, 1710164008931657, 36396070427846536, 810244122520224111, 18833465673721387018, 456310533309915775301, 11505888654389005045548

Offset: 0

Author

Alois P. Heinz, Feb 23 2019

Keywords

• nonn

Links

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

Crossrefs

Column k=6 of A324362.

Cf. A306234.

Programs

Maple

a:= n-> (k-> -add((-1)^j*binomial(n, j)*(n+k-j)!, j=1..n)/k!)(6):
seq(a(n), n=0..23);

Mathematica

With[{nn=20},CoefficientList[Series[(1-Exp[-x])/(1-x)^7,{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Jul 06 2021 *)

Formula

E.g.f.: (1-exp(-x))/(1-x)^7.

a(n) = -1/6! * Sum_{j=1..n} (-1)^j * binomial(n,j) * (n+6-j)!.

a(n) = A306234(n+6,6).