A052806 Number of sequences of rooted identity trees with a total of n nodes.

1, 1, 2, 4, 9, 20, 46, 107, 252, 597, 1425, 3418, 8235, 19910, 48287, 117412, 286150, 698771, 1709403, 4188258, 10276221, 25245406, 62091122, 152872521, 376741574, 929260598, 2293936762, 5666939995, 14009267368, 34654583662, 85775930151, 212428393223

Offset

0,3

Comments

Original name: a simple grammar.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 767

Bernhard Gittenberger, Emma Yu Jin, Michael Wallner, On the shape of random Pólya structures, arXiv:1707.02144 [math.CO], 2017, p. 20.

Formula

G.f.: 1/(1-g(x)) where g(x) is the g.f. of A004111. - Andrew Howroyd, Aug 09 2020

Maple

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

Prog

(PARI) WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, (-1)^(n-1)/n))))-1, -#v)}
seq(n)={my(v=[]); for(n=1, n, v=concat([1], WeighT(v))); Vec(1/(1-x*Ser(v)))} \\ Andrew Howroyd, Aug 09 2020

Crossrefs

Cf. A004111.

Sequence in context: A085748 A317097 A252354 * A329672 A218552 A110198

Adjacent sequences: A052803 A052804 A052805 * A052807 A052808 A052809

Keyword

easy,nonn

Author

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

Extensions

More terms from Eric M. Schmidt, Dec 02 2017

Named changed by Andrew Howroyd, Aug 09 2020

Status

approved