A280779 - OEIS

%I #26 Jan 22 2017 21:25:52

%S 1,1,1,3,3,5,45,315,35,567,2025,7425,467775,6081075,257985,638512875,

%T 638512875,172297125,13956067125,74246277105,3093594879375,

%U 14992036723125,2143861251406875,16436269594119375,4226469324202125,48028060502296875,593531957565421875,56437147443285984375

%N Denominators of coefficients in asymptotic expansion of M_n (number of monolithic chord diagrams, A280775).

%C This has the same start as two other sequences, A241591 and A248592, but appears to be different from both.

%H Gheorghe Coserea, <a href="/A280779/b280779.txt">Table of n, a(n) for n = 0..101</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.

%e Coefficients are 1, -4,-6, -154/3, -1610/3, -34588/5, -4666292/45, -553625626/315, -1158735422/35, ...

%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 seq(N) = {

%o   my(M = subst(x*Ser(A000699_seq(N)), x, x/(1-x)^2));

%o   Vec(x/(1-x)*exp(1-x/2-(1-x)^2/(2*x)*(2*M + M^2))/M);

%o };

%o apply(numerator, seq(18))  \\ _Gheorghe Coserea_, Jan 22 2017

%Y Cf. A000699, A280775, A111111, A280777, A280778, A280780, A280781.

%Y Cf. also A241591, A248592.

%K nonn,frac

%O 0,4

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