A293962 Number of linear chord diagrams having n chords and maximal chord length n, a(0)=1.

1, 1, 2, 10, 70, 630, 6930, 90090, 1351350, 22972950, 436486050, 9166207050, 210822762150, 5270569053750, 142305364451250, 4126855569086250, 127932522641673750, 4221773247175233750, 147762063651133181250, 5467196355091927706250, 213220657848585180543750

Offset: 0

Author

Alois P. Heinz, Oct 20 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..404
• Camille Combe and Samuele Giraudo, Cliff operads: a hierarchy of operads on words, arXiv:2106.14552 [math.CO], 2021.

Crossrefs

Cf. A001147, A293961.

Programs

Maple

a:= proc(n) option remember; `if`(n<3, [1, 1, 2][n+1],
      (2*n-1)*a(n-1))
    end:
seq(a(n), n=0..20);

Formula

E.g.f.: (x + 1 + 2/sqrt(1-2*x))/3.

a(n) = (2*n-1)*a(n-1) for n > 2, a(0) = a(1) = 1, a(2) = 2.

a(n) = 2/3 * A001147(n) = 2/3 * (2n-1)!! for n>1.

a(n) = A293961(n,n).