A022494 Number of connected regular linearized chord diagrams of degree n.

1, 1, 1, 2, 5, 16, 63, 293, 1561, 9321, 61436, 442134, 3446077, 28905485, 259585900, 2485120780, 25267283367, 271949606805, 3089330120711, 36943477086287, 463943009361687, 6105064699310785, 84011389289865102

Offset

0,4

Links

Gheorghe Coserea, Table of n, a(n) for n = 0..202

A. Stoimenow, Enumeration of chord diagrams and an upper bound for Vassiliev invariants, J. Knot Theory Ramifications, 7 (1998), no. 1, 93-114. [broken link], [DOI]

Don Zagier, Vassiliev invariants and a strange identity related to the Dedekind eta-function, Topology, vol.40, pp.945-960 (2001); see p.955.

Prog

(PARI)
A137251_seq(N) = {
  my(x='x + O('x^(N+1)), t='t+O('t^(N+2)), q=1-x, z=1/t-1, p=vector(N+1));
  p[1]=1; for (n=1, #p-1, p[n+1] = p[n] * (1-q^n)/(1+z*q^n));
  apply(p->Vecrev(p), Vec((apply(p->Pol(p, 't), vecsum(p)/(1+z))-'t)/'t^2));
};
A022494_seq(N) = {
  my(s = 't+'t^2*'x*Ser(apply(v->Polrev(v, 't), A137251_seq(N))),
     r = Ser(vector(N+1, n, subst(polcoeff(s, n-1, 't), 'x, 'u + O('u^(N+1)))), 't));
  Vec(1+subst(Pol(t/serreverse(r) - 1, 't), 't, 1));
};
A022494_seq(22) \\ Gheorghe Coserea, Nov 01 2017

Crossrefs

Cf. A137251.

Sequence in context: A112951 A124470 A105072 * A136127 A111004 A344640

Adjacent sequences: A022491 A022492 A022493 * A022495 A022496 A022497

Keyword

nonn

Author

Alexander Stoimenow (stoimeno(AT)math.toronto.edu)

Status

approved