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

1, -4, -6, -154, -1610, -34588, -4666292, -553625626, -1158735422, -388434091184, -31268175015478, -2796356409576766, -4624948938397276052, -1691272281281652408568, -2154089954877183990112, -170222948041126582837968646, -5761785676811885455064909606, -55629298859254851627617870836

Offset

0,2

Links

Gheorghe Coserea, Table of n, a(n) for n = 0..101

Michael Borinsky, Generating asymptotics for factorially divergent sequences, arXiv preprint arXiv:1603.01236 [math.CO], 2016.

Example

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

Prog

(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;
};
seq(N) = {
  my(M = subst(x*Ser(A000699_seq(N)), x, x/(1-x)^2));
  Vec(x/(1-x)*exp(1-x/2-(1-x)^2/(2*x)*(2*M + M^2))/M);
};
apply(numerator, seq(18))  \\ Gheorghe Coserea, Jan 22 2017

Crossrefs

Cf. A000699, A280775, A111111, A280777, A280779, A280780, A280781.

Sequence in context: A176493 A355230 A070155 * A197882 A074124 A303161

Adjacent sequences: A280775 A280776 A280777 * A280779 A280780 A280781

Keyword

sign,frac

Author

N. J. A. Sloane, Jan 19 2017

Extensions

More terms from Gheorghe Coserea, Jan 22 2017

Status

approved