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

1, 2, 8, 16, 128, 1280, 3072, 215040, 3440640, 2293760, 137625600, 201850880, 72666316800, 1889324236800, 52901078630400, 176336928768000, 135426761293824, 191854578499584000, 1593868805996544000, 787371190162292736000, 31494847606491709440000, 29395191099392262144000

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, -5/2, -43/8, -579/16, -44477/128, -5326191/1280, -180306541/3072, ...

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(C = 'x*Ser(A000699_seq(N))); Vec(x*exp(1-(2*C+C^2)/(2*x))/C);
apply(denominator, seq(22)) \\ Gheorghe Coserea, Jan 22 2017

Crossrefs

Cf. A000699, A280775, A111111, A280776, A280778, A280779, A280780, A280781.

Sequence in context: A199043 A046161 A092978 * A013516 A259688 A101059

Adjacent sequences: A280774 A280775 A280776 * A280778 A280779 A280780

Keyword

nonn,frac

Author

N. J. A. Sloane, Jan 19 2017

Extensions

More terms from Gheorghe Coserea, Jan 22 2017

Status

approved