A054358 Number of unlabeled asymmetric 2-ary cacti having n polygons.

1, 1, 0, 1, 2, 8, 18, 61, 170, 538, 1654, 5344, 17252, 57146, 190786, 646305, 2209050, 7626164, 26532732, 93013852, 328196780, 1165060170, 4158266282, 14915635376, 53745892932, 194477856048, 706436256598, 2575316698792, 9419568272632

Offset

0,5

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

Miklos Bona, Michel Bousquet, Gilbert Labelle, and Pierre Leroux, Enumeration of m-ary cacti, Advances in Applied Mathematics, 24 (2000), 22-56.

Index entries for sequences related to cacti

Formula

a(n) = (1/n)*(Sum_{d|n} mu(n/d)*binomial(2*d, d)) - binomial(2*n, n)/(n+1) for n > 0. - Andrew Howroyd, May 02 2018

Mathematica

a[0] = 1; a[n_] := DivisorSum[n, MoebiusMu[n/#] Binomial[2#, #]&]/n - Binomial[2n, n]/(n+1);
Table[a[n], {n, 0, 28}] (* Jean-François Alcover, Jul 01 2018, after Andrew Howroyd *)

Prog

(PARI) a(n) = if(n==0, 1, sumdiv(n, d, moebius(n/d)*binomial(2*d, d))/n - binomial(2*n, n)/(n+1)) \\ Andrew Howroyd, May 02 2018

Crossrefs

Column k=2 of A303913.

Cf. A002995, A054357.

Sequence in context: A358907 A058082 A005675 * A268658 A074128 A061226

Adjacent sequences: A054355 A054356 A054357 * A054359 A054360 A054361

Keyword

nonn

Author

Simon Plouffe

Extensions

More terms from Vladeta Jovovic, Oct 04 2007

Status

approved