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A173841 Number of permutations of 1..n with no adjacent pair summing to n+1. 3
1, 1, 0, 2, 8, 48, 240, 1968, 13824, 140160, 1263360, 15298560, 168422400, 2373073920, 30865121280, 496199854080, 7445355724800, 134510244986880, 2287168006717440, 45877376537395200, 871804170613555200, 19225435113632563200, 403779880746418176000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

If a(n,k) is the number of permutations of 1..n with no adjacent pair summing to n+k, then a(n,k) = a(n,k+1) for n+k even. [proved by William Keith]

LINKS

Table of n, a(n) for n=0..22.

FORMULA

k = 1; a(n,k) = Sum_{j=0..m} (-2)^j*binomial(m,j)*(n-j)! where m = max(0, floor((n-k+1)/2)). [From Max Alekseyev, on the Sequence Fans Mailing List]

CROSSREFS

Sequence in context: A058928 A228288 A292277 * A004141 A009693 A192251

Adjacent sequences:  A173838 A173839 A173840 * A173842 A173843 A173844

KEYWORD

nonn

AUTHOR

R. H. Hardin, Feb 26 2010

EXTENSIONS

More terms from Alois P. Heinz, Jan 09 2017

STATUS

approved

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Last modified March 1 03:32 EST 2021. Contains 341732 sequences. (Running on oeis4.)