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A052843 A simple grammar. 1
1, 1, 2, 3, 6, 10, 20, 38, 79, 162, 348, 751, 1661, 3695, 8335, 18919, 43310, 99664, 230700, 536327, 1252298, 2934508, 6900046, 16272771, 38484608, 91243851, 216839820, 516423974, 1232376315, 2946354649, 7056335478, 16926813939, 40665822366, 97836595223, 235697108115, 568531616730 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) is the number of forests of rooted unlabeled identity trees.  Euler transform of A004111. - Geoffrey Critzer, Oct 13 2012

REFERENCES

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 64, Eq. (3.3.15); p. 80, Problem 3.10.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 811

FORMULA

O.g.f.: prod(n>=1, 1/(1 - x^n)^A004111(n) ). - Geoffrey Critzer, Oct 13 2012

MAPLE

spec := [S, {C=Prod(Z, B), B=PowerSet(C), S=Set(C)}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);

# second Maple program:

with(numtheory):

b:= proc(n) option remember; `if`(n<2, n, add(b(n-k)*add(d*

       b(d)*(-1)^(k/d+1), d=divisors(k)), k=1..n-1)/(n-1))

    end:

a:= proc(n) option remember; `if`(n=0, 1, add(add(d*b(d),

       d=divisors(j)) *a(n-j), j=1..n)/n)

    end:

seq(a(n), n=0..40);  # Alois P. Heinz, Mar 06 2015

MATHEMATICA

nn=35; s[n_, k_]:=s[n, k]=a[n+1-k]+If[n<2k, 0, -s[n-k, k]]; a[1]=1; a[n_]:=a[n]=Sum[a[i]s[n-1, i]i, {i, 1, n-1}]/(n-1); it=Table[a[i], {i, 1, nn}]; CoefficientList[Series[Product[1/(1-x^i)^it[[i]], {i, 1, nn}], {x, 0, nn}], x]  (* after code given by Robert A. Russell in A004111 *)

(* Geoffrey Critzer, Oct 13 2012 *)

CROSSREFS

Cf. A004111.

Sequence in context: A123423 A005195 A228835 * A120707 A047111 A106741

Adjacent sequences:  A052840 A052841 A052842 * A052844 A052845 A052846

KEYWORD

easy,nonn

AUTHOR

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

EXTENSIONS

Added more terms, Geoffrey Critzer, Oct 13 2012

STATUS

approved

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Last modified January 19 09:35 EST 2020. Contains 331048 sequences. (Running on oeis4.)