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A309242 a(n) is the smallest integer m such that the equality Product_{i=1..n} (x_i + m) = (m+n)!/m! for integers x_1, ..., x_n from N = { 1, 2, ..., n } guarantees that they form a permutation of N.

%I A309242 #28 Jan 03 2021 13:05:32
%S A309242 0,0,0,1,2,5,6,9,10,16,18,27,28,33,45,45,45,56,78,81,108,120,136,140,
%T A309242 180,180,192,209,210,280,280,286,325,325,380,392,527,527,527,625,650,
%U A309242 650,703,703
%N A309242 a(n) is the smallest integer m such that the equality Product_{i=1..n} (x_i + m) = (m+n)!/m! for integers x_1, ..., x_n from N = { 1, 2, ..., n } guarantees that they form a permutation of N.
%C A309242 a(n) <= A065048(n) + 1.
%H A309242 JPF et al., <a href="https://mathoverflow.net/q/336273">A necessary and sufficient condition for (x_1,...,x_n) to be a permutation of (1,...,n)</a>. MathOverflow, 2019.
%K A309242 nonn,more
%O A309242 1,5
%A A309242 _Max Alekseyev_, Jul 17 2019