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

%I M2680

%S 0,1,1,1,3,7,21,61,187,577,1825,5831,18883,61699,203429,675545,

%T 2258291,7592249,25656477,87096661,296891287,1015797379,3487272317,

%U 12008898531,41471260883,143588078449,498343911529,1733410858955,6041795275027,21098924740155

%N Number of asymmetric permutation rooted trees with n nodes.

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

%H Alois P. Heinz, <a href="/A005355/b005355.txt">Table of n, a(n) for n = 0..1000</a>

%H Gilbert Labelle, <a href="http://dx.doi.org/10.1016/0747-7171(92)90037-5">Counting asymmetric enriched trees</a>, J. Symbolic Comput. 14 (1992), no. 2-3, 211-242.

%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>

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

%t 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-Fran├žois Alcover_, Jan 04 2016 *)

%Y Cf. A004111, A050383.

%K nonn,nice,easy,eigen

%O 0,5

%A _N. J. A. Sloane_, _Simon Plouffe_, _Susanna Cuyler_

%E More terms, formula from _Christian G. Bower_, Nov 15 1999

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Last modified May 10 04:37 EDT 2021. Contains 343748 sequences. (Running on oeis4.)