A005355 Number of asymmetric permutation rooted trees with n nodes. (Formerly M2680)

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

0,5

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

Formula

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

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 *)

Crossrefs

Cf. A004111, A050383.

Sequence in context: A102877 A122983 A351822 * A182399 A025235 A129366

Adjacent sequences: A005352 A005353 A005354 * A005356 A005357 A005358

Keyword

nonn,nice,easy,eigen

Author

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

Extensions

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

Status

approved