A005355 Number of asymmetric permutation rooted trees with n nodes.

0, 1, 1, 1, 3, 7, 21, 61, 187, 577, 1825, 5831, 18883, 61699, 203429, 675545, 2258291, 7592249, 25656477, 87096661, 296891287, 1015797379, 3487272317, 12008898531, 41471260883, 143588078449, 498343911529, 1733410858955, 6041795275027, 21098924740155

Offset: 0

Author

N. J. A. Sloane, Simon Plouffe, Susanna Cuyler

Keywords

• nonn
• nice
• easy
• eigen

References

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Gilbert Labelle, Counting asymmetric enriched trees, J. Symbolic Comput. 14 (1992), no. 2-3, 211-242.
• Index entries for sequences related to rooted trees

Crossrefs

Cf. A004111, A050383.

Programs

Mathematica

a[0] = 1; a[1] = 1; a[n_] := a[n] = Sum[a[k]*a[n-k], {k, 1, n-1}] - If[EvenQ[n-1], a[(n-1)/2], 0]; Table[a[n], {n, 0, 27}] (* Jean-François Alcover, Jan 04 2016 *)

Formula

Shifts left under transform T where Ta has g.f. (1-A(x^2))/(1-A(x)).

Extensions

More terms, formula from Christian G. Bower, Nov 15 1999