A322059 Expansion of generating function related to a certain class of combinatorial objects.

1, 3, 8, 21, 50, 128

Offset: 1

Author

N. J. A. Sloane, Dec 25 2018

Keywords

• nonn
• more

Comments

For precise definition see Example 15.3.6 of Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, pages 1001-1002.

Apparently this has been computed by series inversion (INVERT transform) of the generating function x+2*x^2+3*x^3+4*x^4, which is not related to a Cyc. transformation (as claimed by Bona) (??) To obtain an interpretation from the Polya cycle index for the group of cyclic permutations, one would have to plug in the g.f. x+2*x^2+5*x^3+10*x^4+18*x^5+26*x^6+.. and it's difficult to associate this with any sort of marked linear chains of length up to 4 (because terms of x^5 and higher are needed). - R. J. Mathar, Feb 06 2025

Links

• N.Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, pages 1001-1002.
• Miklos Bona, editor, Handbook of Enumerative Combinatorics, errata.
• N. J. A. Sloane, Annotated scan of page 1001 of Bona (2015).
• N. J. A. Sloane, Annotated scan of page 1002 of Bona (2015).

Crossrefs

Cf. A322060, A380886 (column 4), A380890 (cycles of rooted chains), A032198 (cycles of directed linear chains), A002861 (cycles of rooted trees).