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A301802 Number of permutations of {1, 2, ..., n} such that no k+2 points lie on a polynomial of degree k.

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%I A301802 #18 Apr 08 2018 04:36:58
%S A301802 1,1,2,4,18,48,216,584,2870,10408,45244,160248,762554
%N A301802 Number of permutations of {1, 2, ..., n} such that no k+2 points lie on a polynomial of degree k.
%C A301802 a(n) is even for all n > 1.
%C A301802 Is this sequence strictly increasing for n > 0?
%H A301802 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 A301802 For n = 4, the 18 different permutations are:
%e A301802 [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 A301802 [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 A301802 [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 A301802 Cf. A300002.
%K A301802 nonn,more
%O A301802 0,3
%A A301802 _Peter Kagey_, Mar 26 2018
%E A301802 a(0) and a(10)-a(12) from _Peter J. Taylor_, Mar 28 2018