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A280778 Numerators of coefficients in asymptotic expansion of M_n (number of monolithic chord diagrams, A280775).

%I A280778 #27 Jan 22 2017 21:41:09
%S A280778 1,-4,-6,-154,-1610,-34588,-4666292,-553625626,-1158735422,
%T A280778 -388434091184,-31268175015478,-2796356409576766,-4624948938397276052,
%U A280778 -1691272281281652408568,-2154089954877183990112,-170222948041126582837968646,-5761785676811885455064909606,-55629298859254851627617870836
%N A280778 Numerators of coefficients in asymptotic expansion of M_n (number of monolithic chord diagrams, A280775).
%H A280778 Gheorghe Coserea, <a href="/A280778/b280778.txt">Table of n, a(n) for n = 0..101</a>
%H A280778 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 A280778 Coefficients are 1, -4, -6, -154/3, -1610/3, -34588/5, -4666292/45, -553625626/315, -1158735422/35, ...
%o A280778 (PARI)
%o A280778 A000699_seq(N) = {
%o A280778   my(a = vector(N)); a[1] = 1;
%o A280778   for (n=2, N, a[n] = sum(k=1, n-1, (2*k-1)*a[k]*a[n-k])); a;
%o A280778 };
%o A280778 seq(N) = {
%o A280778   my(M = subst(x*Ser(A000699_seq(N)), x, x/(1-x)^2));
%o A280778   Vec(x/(1-x)*exp(1-x/2-(1-x)^2/(2*x)*(2*M + M^2))/M);
%o A280778 };
%o A280778 apply(numerator, seq(18))  \\ _Gheorghe Coserea_, Jan 22 2017
%Y A280778 Cf. A000699, A280775, A111111, A280777, A280779, A280780, A280781.
%K A280778 sign,frac
%O A280778 0,2
%A A280778 _N. J. A. Sloane_, Jan 19 2017
%E A280778 More terms from _Gheorghe Coserea_, Jan 22 2017