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A022494 Number of connected regular linearized chord diagrams of degree n. 1
1, 1, 1, 2, 5, 16, 63, 293, 1561, 9321, 61436, 442134, 3446077, 28905485, 259585900, 2485120780, 25267283367, 271949606805, 3089330120711, 36943477086287, 463943009361687, 6105064699310785, 84011389289865102 (list; graph; refs; listen; history; text; internal format)
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 A079566

Adjacent sequences:  A022491 A022492 A022493 * A022495 A022496 A022497

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified November 20 14:54 EST 2019. Contains 329337 sequences. (Running on oeis4.)