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.

0, 0, 0, 1, 2, 5, 6, 9, 10, 16, 18, 27, 28, 33, 45, 45, 45, 56, 78, 81, 108, 120, 136, 140, 180, 180, 192, 209, 210, 280, 280, 286, 325, 325, 380, 392, 527, 527, 527, 625, 650, 650, 703, 703

Offset: 1

Author

Max Alekseyev, Jul 17 2019

Keywords

• nonn
• more

Comments

a(n) <= A065048(n) + 1.

Links

• JPF et al., A necessary and sufficient condition for (x_1,...,x_n) to be a permutation of (1,...,n). MathOverflow, 2019.