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A054370 Number of unlabeled asymmetric 7-ary cacti having n polygons. 4
1, 1, 0, 21, 182, 2093, 23394, 285383, 3621150, 47813367, 650302814, 9066061193, 128986881660, 1866877313441, 27417577343674, 407771633368995, 6131640430397790, 93096368350684720, 1425633583562073228, 21998953427963954547, 341803226976420690600 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

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

Index entries for sequences related to cacti

FORMULA

a(n) = (1/n)*(Sum_{d|n} mu(n/d)*binomial(7*d, d)) - 6*binomial(7*n, n)/(6*n+1) for n > 0. - Andrew Howroyd, May 02 2018

MATHEMATICA

a[0] = 1;

a[n_] := DivisorSum[n, MoebiusMu[n/#] Binomial[7#, #]&]/n - 6 Binomial[7n, n]/(6n + 1);

Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Jul 01 2018, after Andrew Howroyd *)

PROG

(PARI) a(n) = if(n==0, 1, sumdiv(n, d, moebius(n/d)*binomial(7*d, d))/n - 6*binomial(7*n, n)/(6*n+1)) \\ Andrew Howroyd, May 02 2018

CROSSREFS

Column k=7 of A303913.

Cf. A054369, A054371.

Sequence in context: A219412 A062159 A059721 * A219171 A232045 A302162

Adjacent sequences:  A054367 A054368 A054369 * A054371 A054372 A054373

KEYWORD

nonn

AUTHOR

Simon Plouffe

EXTENSIONS

Terms a(11) and beyond from Andrew Howroyd, May 02 2018

STATUS

approved

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Last modified February 29 08:26 EST 2020. Contains 332355 sequences. (Running on oeis4.)