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

%I A293962 #12 Oct 21 2021 01:11:08
%S A293962 1,1,2,10,70,630,6930,90090,1351350,22972950,436486050,9166207050,
%T A293962 210822762150,5270569053750,142305364451250,4126855569086250,
%U A293962 127932522641673750,4221773247175233750,147762063651133181250,5467196355091927706250,213220657848585180543750
%N A293962 Number of linear chord diagrams having n chords and maximal chord length n, a(0)=1.
%H A293962 Alois P. Heinz, <a href="/A293962/b293962.txt">Table of n, a(n) for n = 0..404</a>
%H A293962 Camille Combe and Samuele Giraudo, <a href="https://arxiv.org/abs/2106.14552">Cliff operads: a hierarchy of operads on words</a>, arXiv:2106.14552 [math.CO], 2021.
%F A293962 E.g.f.: (x + 1 + 2/sqrt(1-2*x))/3.
%F A293962 a(n) = (2*n-1)*a(n-1) for n > 2, a(0) = a(1) = 1, a(2) = 2.
%F A293962 a(n) = 2/3 * A001147(n) = 2/3 * (2n-1)!! for n>1.
%F A293962 a(n) = A293961(n,n).
%p A293962 a:= proc(n) option remember; `if`(n<3, [1, 1, 2][n+1],
%p A293962       (2*n-1)*a(n-1))
%p A293962     end:
%p A293962 seq(a(n), n=0..20);
%Y A293962 Cf. A001147, A293961.
%K A293962 nonn
%O A293962 0,3
%A A293962 _Alois P. Heinz_, Oct 20 2017