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A280920 Seventh column of Euler's difference table in A068106. 2
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
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
KEYWORD
nonn
AUTHOR
Enrique Navarrete, Jan 10 2017
STATUS
approved

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Last modified March 4 13:28 EST 2024. Contains 370532 sequences. (Running on oeis4.)