A280920 Seventh column of Euler's difference table in A068106.

0, 0, 0, 0, 0, 720, 4320, 30960, 256320, 2399760, 25022880, 287250480, 3597143040, 48773612880, 711607724640, 11113078385520, 184925331414720, 3265974496290960, 61006644910213920, 1201583921745846960, 24885771463659934080, 540624959563046320080, 12291921453805577987040

Offset

1,6

Comments

For n >= 7, this is the number of permutations of [n] that avoid substrings j(j+6), 1 <= j <= n-6.

Links

Indranil Ghosh, Table of n, a(n) for n = 1..400

Enrique Navarrete, Generalized K-Shift Forbidden Substrings in Permutations, arXiv:1610.06217 [math.CO], 2016.

Formula

For n>=7: a(n) = Sum_{j=0..n-6} (-1)^j*binomial(n-6,j)*(n-j)!.

Note a(n)/n! ~ 1/e.

Example

a(10)=2399760 since there are 2399760 permutations in S10 that avoid substrings {17,28,39,4(10)}.

Mathematica

Table[Sum[(-1)^j*Binomial[n-6, j]*(n-j)!, {j, 0, n-6}], {n, 1, 23}] (* Indranil Ghosh, Feb 26 2017 *)

Prog

(Python)
f=math.factorial
def C(n, r):return f(n)/f(r)/f(n-r)
def A280920(n):
....s=0
....for j in range(0, n-5):
........s+=(-1)**j*C(n-6, j)*f(n-j)
....return s # Indranil Ghosh, Feb 26 2017
(PARI) a(n) = sum(j=0, n-6, (-1)^j*binomial(n-6, j)*(n-j)!); \\ Michel Marcus, Feb 26 2017

Crossrefs

Also 720 times A176732.

Cf. A068106.

Sequence in context: A167563 A202095 A233787 * A187290 A218487 A053625

Adjacent sequences: A280917 A280918 A280919 * A280921 A280922 A280923

Keyword

nonn

Author

Enrique Navarrete, Jan 10 2017

Status

approved