A054364 Number of unlabeled asymmetric 5-ary cacti having n polygons.

1, 1, 0, 10, 60, 505, 3876, 33125, 290700, 2661100, 25049020, 241724375, 2379812100, 23833198135, 242172147380, 2491817140380, 25921361665100, 272256630756260, 2884054853862540, 30784716141936520, 330853931834416520, 3577823885432126890, 38907658110093347780

Offset

0,4

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(5*d, d)) - 4*binomial(5*n, n)/(4*n+1) for n > 0. - Andrew Howroyd, May 02 2018

Mathematica

a[0] = 1;
a[n_] := DivisorSum[n, MoebiusMu[n/#] Binomial[5#, #]&]/n - 4 Binomial[5n, n]/(4n+1);
Table[a[n], {n, 0, 22}] (* Jean-François Alcover, Jul 01 2018, after Andrew Howroyd *)

Prog

(PARI) a(n) = if(n==0, 1, sumdiv(n, d, moebius(n/d)*binomial(5*d, d))/n - 4*binomial(5*n, n)/(4*n+1)) \\ Andrew Howroyd, May 02 2018

Crossrefs

Column k=5 of A303913.

Cf. A054363, A054365.

Sequence in context: A155633 A368525 A002493 * A004309 A281863 A219368

Adjacent sequences: A054361 A054362 A054363 * A054365 A054366 A054367

Keyword

nonn

Author

Simon Plouffe

Extensions

Terms a(13) and beyond from Andrew Howroyd, May 02 2018

Status

approved