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A280920 Seventh column of Euler's difference table in A068106. 1
0, 0, 0, 0, 0, 720, 4320, 30960, 256320, 2399760, 25022880, 287250480, 3597143040, 48773612880, 711607724640, 11113078385520, 184925331414720, 3265974496290960, 61006644910213920, 1201583921745846960, 24885771463659934080, 540624959563046320080, 12291921453805577987040 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 6 01:25 EST 2021. Contains 349558 sequences. (Running on oeis4.)