# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a052843 Showing 1-1 of 1 %I A052843 #22 Apr 18 2017 07:04:11 %S A052843 1,1,2,3,6,10,20,38,79,162,348,751,1661,3695,8335,18919,43310,99664, %T A052843 230700,536327,1252298,2934508,6900046,16272771,38484608,91243851, %U A052843 216839820,516423974,1232376315,2946354649,7056335478,16926813939,40665822366,97836595223,235697108115,568531616730 %N A052843 A simple grammar. %C A052843 a(n) is the number of forests of rooted unlabeled identity trees. Euler transform of A004111. - _Geoffrey Critzer_, Oct 13 2012 %D A052843 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 64, Eq. (3.3.15); p. 80, Problem 3.10. %H A052843 Alois P. Heinz, Table of n, a(n) for n = 0..1000 %H A052843 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 811 %F A052843 O.g.f.: prod(n>=1, 1/(1 - x^n)^A004111(n) ). - _Geoffrey Critzer_, Oct 13 2012 %p A052843 spec := [S,{C=Prod(Z,B),B=PowerSet(C),S=Set(C)},unlabeled]: seq(combstruct[count](spec,size=n), n=0..20); %p A052843 # second Maple program: %p A052843 with(numtheory): %p A052843 b:= proc(n) option remember; `if`(n<2, n, add(b(n-k)*add(d* %p A052843 b(d)*(-1)^(k/d+1), d=divisors(k)), k=1..n-1)/(n-1)) %p A052843 end: %p A052843 a:= proc(n) option remember; `if`(n=0, 1, add(add(d*b(d), %p A052843 d=divisors(j)) *a(n-j), j=1..n)/n) %p A052843 end: %p A052843 seq(a(n), n=0..40); # _Alois P. Heinz_, Mar 06 2015 %t A052843 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 *) %t A052843 (* _Geoffrey Critzer_, Oct 13 2012 *) %Y A052843 Cf. A004111. %K A052843 easy,nonn %O A052843 0,3 %A A052843 encyclopedia(AT)pommard.inria.fr, Jan 25 2000 %E A052843 Added more terms, _Geoffrey Critzer_, Oct 13 2012 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE