A052806 - OEIS

%I #15 Aug 10 2020 00:21:14

%S 1,1,2,4,9,20,46,107,252,597,1425,3418,8235,19910,48287,117412,286150,

%T 698771,1709403,4188258,10276221,25245406,62091122,152872521,

%U 376741574,929260598,2293936762,5666939995,14009267368,34654583662,85775930151,212428393223

%N Number of sequences of rooted identity trees with a total of n nodes.

%C Original name: a simple grammar.

%H Andrew Howroyd, <a href="/A052806/b052806.txt">Table of n, a(n) for n = 0..500</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=767">Encyclopedia of Combinatorial Structures 767</a>

%H Bernhard Gittenberger, Emma Yu Jin, Michael Wallner, <a href="https://arxiv.org/abs/1707.02144">On the shape of random Pólya structures</a>, arXiv:1707.02144 [math.CO], 2017, p. 20.

%F G.f.: 1/(1-g(x)) where g(x) is the g.f. of A004111. - _Andrew Howroyd_, Aug 09 2020

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

%o (PARI) WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v,n,(-1)^(n-1)/n))))-1,-#v)}

%o seq(n)={my(v=[]); for(n=1, n, v=concat([1],WeighT(v))); Vec(1/(1-x*Ser(v)))} \\ _Andrew Howroyd_, Aug 09 2020

%Y Cf. A004111.

%K easy,nonn

%O 0,3

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

%E More terms from _Eric M. Schmidt_, Dec 02 2017

%E Named changed by _Andrew Howroyd_, Aug 09 2020