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A322059
Expansion of generating function related to a certain class of combinatorial objects.
5
1, 3, 8, 21, 50, 128
OFFSET
1,2
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.
CROSSREFS
Cf. A322060, A380886 (column 4), A380890 (cycles of rooted chains), A032198 (cycles of directed linear chains), A002861 (cycles of rooted trees).
Sequence in context: A363601 A193045 A238831 * A259714 A096770 A007835
KEYWORD
nonn,more
AUTHOR
N. J. A. Sloane, Dec 25 2018
STATUS
approved