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A324356 Total number of occurrences of 6 in the (signed) displacement sets of all permutations of [n+6] divided by 6!. 3
0, 1, 13, 148, 1707, 20686, 266321, 3652608, 53339831, 827870338, 13624599309, 237169578724, 4356110013107, 84220077081414, 1710164008931657, 36396070427846536, 810244122520224111, 18833465673721387018, 456310533309915775301, 11505888654389005045548 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 25 17:22 EDT 2021. Contains 348255 sequences. (Running on oeis4.)