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URL: https://oeis.org/A052806

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A052806
Number of sequences of rooted identity trees with a total of n nodes.
1
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
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
KEYWORD
easy,nonn
EXTENSIONS
More terms from Eric M. Schmidt, Dec 02 2017
Named changed by Andrew Howroyd, Aug 09 2020
STATUS
approved