A280779 Denominators of coefficients in asymptotic expansion of M_n (number of monolithic chord diagrams, A280775).

1, 1, 1, 3, 3, 5, 45, 315, 35, 567, 2025, 7425, 467775, 6081075, 257985, 638512875, 638512875, 172297125, 13956067125, 74246277105, 3093594879375, 14992036723125, 2143861251406875, 16436269594119375, 4226469324202125, 48028060502296875, 593531957565421875, 56437147443285984375

Offset

0,4

Comments

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

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, A280778, A280780, A280781.

Cf. also A241591, A248592.

Sequence in context: A256402 A170919 A364661 * A241591 A248592 A132809

Adjacent sequences: A280776 A280777 A280778 * A280780 A280781 A280782

Keyword

nonn,frac

Author

N. J. A. Sloane, Jan 19 2017

Status

approved