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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.

LINKS

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

FORMULA

k = 1; m = \max (0,floor((n-k+1)/2)); a(n,k) = \sum_{j=0}^m (-2)^j \binom{m}{j} (n-j)!

CROSSREFS

Sequence in context: A193944 A058928 A228288 * A004141 A009693 A192251

Adjacent sequences:  A173838 A173839 A173840 * A173842 A173843 A173844

KEYWORD

nonn

AUTHOR

R. H. Hardin Feb 26 2010, comment proved by William Keith, formula from Max Alekseyev, on the Sequence Fans Mailing List

EXTENSIONS

More terms from Alois P. Heinz, Jan 09 2017

STATUS

approved

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Last modified June 27 11:25 EDT 2017. Contains 288788 sequences.