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%I #18 Apr 08 2018 04:36:58
%S 1,1,2,4,18,48,216,584,2870,10408,45244,160248,762554
%N Number of permutations of {1, 2, ..., n} such that no k+2 points lie on a polynomial of degree k.
%C a(n) is even for all n > 1.
%C Is this sequence strictly increasing for n > 0?
%H Programming Puzzles & Code Golf Stack Exchange, <a href="https://codegolf.stackexchange.com/q/160382/53884">Permutations such that no k+2 points fall on any polynomial of degree k</a>
%e For n = 4, the 18 different permutations are:
%e [1,2,4,3],[1,3,2,4],[1,3,4,2],[1,4,2,3],[2,1,3,4],[2,1,4,3],
%e [2,3,1,4],[2,4,1,3],[2,4,3,1],[3,1,2,4],[3,1,4,2],[3,2,4,1],
%e [3,4,1,2],[3,4,2,1],[4,1,3,2],[4,2,1,3],[4,2,3,1],[4,3,1,2].
%Y Cf. A300002.
%K nonn,more
%O 0,3
%A _Peter Kagey_, Mar 26 2018
%E a(0) and a(10)-a(12) from _Peter J. Taylor_, Mar 28 2018
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