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

0,3

Links

Table of n, a(n) for n=0..23.

K. Archer and R. P. Laudone, Pattern avoidance in non-crossing and non-nesting permutations, arXiv:2502.13309 [math.CO], 2025.

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.

Crossrefs

Cf. A383770.

Sequence in context: A261490 A277956 A307678 * A151382 A234958 A188675

Adjacent sequences: A383768 A383769 A383770 * A383772 A383773 A383774

Keyword

nonn

Author

Robert P. Laudone, May 09 2025

Status

approved