A005227 Number of atomic species of degree n which are not nontrivial substitutions.
0, 1, 1, 2, 4, 6, 19, 20, 111, 116, 567, 641, 4718, 4772, 35489, 46012, 389277, 487408, 4616580
Offset: 0
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
- 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& J. Labelle, Espèces sur les petites cardinalités Tableaux divers, Université du Québec à Montréal (octobre 1988), Unpublished.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.
Crossrefs
Cf. A005226.
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
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