A383771 Number of noncrossing permutations of [n] avoiding 213 (and by symmetry 132, 213, or 312).
1, 1, 4, 19, 102, 590, 3588, 22617, 146460, 968520, 6513034, 44403604, 306209746, 2132165062, 14970030506, 105862919427, 753344866662, 5390772814578, 38765692377100, 279999861952626, 2030439981144348, 14776796428607224, 107891287190000212, 790105506941871258
Offset: 0
Keywords
Links
- K. Archer and R. P. Laudone, Pattern avoidance in non-crossing and non-nesting permutations, arXiv:2502.13309 [math.CO], 2025.
Crossrefs
Cf. A383770.
Formula
G.f.: A(x) satisfies x^2*A(x)^4 - (x^2+x)*A(x)^3 - x*A(x)^2 + (x+1)*A(x) - 1 = 0.