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A280775 Number of monolithic chord diagrams with n chords. 7

%I

%S 1,3,11,65,573,6547,89639,1414417,25148617,496416579,10762275539,

%T 254153371121,6494217863461,178558132802259,5257524611172751,

%U 165089697983580641,5507950426778674129,194605351254360182403,7259714571747394749147,285174902634083710549601

%N Number of monolithic chord diagrams with n chords.

%H Gheorghe Coserea, <a href="/A280775/b280775.txt">Table of n, a(n) for n = 1..200</a>

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

%t terms = 20;

%t c[_] = 0;

%t Do[c[x_] = x + x^2*D[c[x]^2/x, x] + O[x]^(terms+1) // Normal, terms];

%t c[x/(1-x)^2] + O[x]^(terms+1) // CoefficientList[#, x]& // Rest (* _Jean-Fran├žois Alcover_, Sep 01 2018 *)

%o (PARI)

%o A000699_seq(N) = {

%o my(a = vector(N)); a[1] = 1;

%o for (n=2, N, a[n] = sum(k=1, n-1, (2*k-1)*a[k]*a[n-k])); a;

%o };

%o N = 20; Vec(subst(x*Ser(A000699_seq(N)), x, x/(1-x)^2)) \\ _Gheorghe Coserea_, Jan 22 2017

%Y Cf. A000699.

%K nonn,changed

%O 1,2

%A _N. J. A. Sloane_, Jan 19 2017

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Last modified December 15 11:05 EST 2018. Contains 318148 sequences. (Running on oeis4.)