A005227 - OEIS

A005227

Number of atomic species of degree n which are not nontrivial substitutions.
(Formerly M1029)

0, 1, 1, 2, 4, 6, 19, 20, 111, 116, 567, 641, 4718, 4772, 35489, 46012, 389277, 487408, 4616580

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

REFERENCES

Labelle, Jacques. Quelques espèces sur les ensembles de petite cardinalité, Ann. Sc. Math. Québec 9.1 (1985): 31-58.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..18.

H. Decoste, G. Labelle, & J. Labelle, Espèces sur les petites cardinalités Tableaux divers, Université du Québec à Montréal (octobre 1988), Unpublished.

Jacques Labelle, Quelques espèces sur les ensembles de petite cardinalité, Ann. Sc. Math. Québec 9.1 (1985): 31-58. (Annotated scanned copy of preprint)

J. Labelle and Y. N. Yeh, The relation between Burnside rings and combinatorial species, J. Combin. Theory, A 50 (1989), 269-284.

FORMULA

Define b(n), c(n), d(n): b(1)=d(1)=0. b(k)=a(k), k>1. c(k)=A000638(k), k>0, d(k)=A005226(k), k>1. d is Dirichlet convolution of b and c. - Christian G. Bower, Feb 23 2006

CROSSREFS

Cf. A005226.

Sequence in context: A294447 A143085 A304756 * A185185 A234019 A279188

Adjacent sequences: A005224 A005225 A005226 * A005228 A005229 A005230

KEYWORD

nonn,hard,more

AUTHOR

N. J. A. Sloane

EXTENSIONS

a(8), a(11) corrected and a(12) added by Christian G. Bower, Feb 23 2006 based on Goetz Pfeiffer's edit to A000638

a(13)-a(18) from Vaclav Kotesovec, Jul 18 2022

STATUS

approved