cp's OEIS Frontend

A280777 Denominators of coefficients in asymptotic expansion of C_n (number of connected chord diagrams, A000699).

%I A280777 #25 Jan 22 2017 21:24:16
%S A280777 1,2,8,16,128,1280,3072,215040,3440640,2293760,137625600,201850880,
%T A280777 72666316800,1889324236800,52901078630400,176336928768000,
%U A280777 135426761293824,191854578499584000,1593868805996544000,787371190162292736000,31494847606491709440000,29395191099392262144000
%N A280777 Denominators of coefficients in asymptotic expansion of C_n (number of connected chord diagrams, A000699).
%H A280777 Gheorghe Coserea, <a href="/A280777/b280777.txt">Table of n, a(n) for n = 0..101</a>
%H A280777 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.
%e A280777 Coefficients are 1, -5/2, -43/8, -579/16, -44477/128, -5326191/1280, -180306541/3072, ...
%o A280777 (PARI)
%o A280777 A000699_seq(N) = {
%o A280777   my(a = vector(N)); a[1] = 1;
%o A280777   for (n=2, N, a[n] = sum(k=1, n-1, (2*k-1)*a[k]*a[n-k])); a;
%o A280777 };
%o A280777 seq(N) = my(C = 'x*Ser(A000699_seq(N))); Vec(x*exp(1-(2*C+C^2)/(2*x))/C);
%o A280777 apply(denominator, seq(22)) \\ _Gheorghe Coserea_, Jan 22 2017
%Y A280777 Cf. A000699, A280775, A111111, A280776, A280778, A280779, A280780, A280781.
%K A280777 nonn,frac
%O A280777 0,2
%A A280777 _N. J. A. Sloane_, Jan 19 2017
%E A280777 More terms from _Gheorghe Coserea_, Jan 22 2017