The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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). 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 EXTENSIONS Terms a(11) and beyond from Andrew Howroyd, May 02 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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