cp's OEIS Frontend

A280775 Number of monolithic chord diagrams with n chords.

%I A280775 #17 Dec 05 2018 09:32:46
%S A280775 1,3,11,65,573,6547,89639,1414417,25148617,496416579,10762275539,
%T A280775 254153371121,6494217863461,178558132802259,5257524611172751,
%U A280775 165089697983580641,5507950426778674129,194605351254360182403,7259714571747394749147,285174902634083710549601
%N A280775 Number of monolithic chord diagrams with n chords.
%H A280775 Gheorghe Coserea, <a href="/A280775/b280775.txt">Table of n, a(n) for n = 1..200</a>
%H A280775 Michael Borinsky, <a href="https://arxiv.org/abs/1603.01236">Generating asymptotics for factorially divergent sequences</a>, arXiv preprint arXiv:1603.01236 [math.CO], 2016. See M_n.
%F A280775 G.f.: C(x/(1-x)^2), where C(x) is the g.f. for A000699.
%t A280775 terms = 20;
%t A280775 c[_] = 0;
%t A280775 Do[c[x_] = x + x^2*D[c[x]^2/x, x] + O[x]^(terms+1) // Normal, terms];
%t A280775 c[x/(1-x)^2] + O[x]^(terms+1) // CoefficientList[#, x]& // Rest (* _Jean-François Alcover_, Sep 01 2018 *)
%o A280775 (PARI)
%o A280775 A000699_seq(N) = {
%o A280775   my(a = vector(N)); a[1] = 1;
%o A280775   for (n=2, N, a[n] = sum(k=1, n-1, (2*k-1)*a[k]*a[n-k])); a;
%o A280775 };
%o A280775 N = 20; Vec(subst(x*Ser(A000699_seq(N)), x, x/(1-x)^2))  \\ _Gheorghe Coserea_, Jan 22 2017
%Y A280775 Cf. A000699.
%K A280775 nonn
%O A280775 1,2
%A A280775 _N. J. A. Sloane_, Jan 19 2017