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

0,3

Links

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

Wikipedia, Permutation

Formula

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

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

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

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 *)

Crossrefs

Column k=6 of A324362.

Cf. A306234.

Sequence in context: A332691 A210165 A132156 * A210158 A130611 A127747

Adjacent sequences: A324353 A324354 A324355 * A324357 A324358 A324359

Keyword

nonn

Author

Alois P. Heinz, Feb 23 2019

Status

approved