A280775 Number of monolithic chord diagrams with n chords.

1, 3, 11, 65, 573, 6547, 89639, 1414417, 25148617, 496416579, 10762275539, 254153371121, 6494217863461, 178558132802259, 5257524611172751, 165089697983580641, 5507950426778674129, 194605351254360182403, 7259714571747394749147, 285174902634083710549601

Offset: 1

Author

N. J. A. Sloane, Jan 19 2017

Keywords

• nonn

Links

• Gheorghe Coserea, Table of n, a(n) for n = 1..200
• Michael Borinsky, Generating asymptotics for factorially divergent sequences, arXiv preprint arXiv:1603.01236 [math.CO], 2016. See M_n.

Crossrefs

Cf. A000699.

Programs

Mathematica

terms = 20;
c[_] = 0;
Do[c[x_] = x + x^2*D[c[x]^2/x, x] + O[x]^(terms+1) // Normal, terms];
c[x/(1-x)^2] + O[x]^(terms+1) // CoefficientList[#, x]& // Rest (* Jean-François Alcover, Sep 01 2018 *)

PARI

A000699_seq(N) = {
  my(a = vector(N)); a[1] = 1;
  for (n=2, N, a[n] = sum(k=1, n-1, (2*k-1)*a[k]*a[n-k])); a;
};
N = 20; Vec(subst(x*Ser(A000699_seq(N)), x, x/(1-x)^2))  \\ Gheorghe Coserea, Jan 22 2017

Formula

G.f.: C(x/(1-x)^2), where C(x) is the g.f. for A000699.