%I #24 Mar 01 2016 03:15:38

%S 2,4,10,36,132,532,2222,9584,42248,189776,864830,3989656,18593424,

%T 87413444,414060796,1974260912,9467922870,45638482068,221001289714,

%U 1074591477112,5244497440468,25681907242416,126149132242490,621386729646752,3068748094479108

%N Number of rooted identity trees with 2-colored nodes.

%C Shifts left and halves under Weigh transform.

%H Alois P. Heinz, <a href="/A038077/b038077.txt">Table of n, a(n) for n = 1..500</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

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

%F a(n) = 2 * A005753(n).

%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

%p add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))

%p end:

%p a:= n-> `if`(n=1, 2, 2*b((n-1)$2)):

%p seq(a(n), n=1..40); # _Alois P. Heinz_, May 20 2013

%t b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, Sum[Binomial[a[i], j]*b[n - i*j, i-1], {j, 0, n/i}]]];

%t a[n_] := If[n==1, 2, 2*b[n-1, n-1]];

%t Table[a[n], {n, 1, 40}] (* _Jean-François Alcover_, Mar 01 2016, after _Alois P. Heinz_ *)

%Y Cf. A004111, A038078, A038079, A038080, A246312.

%K nonn,eigen

%O 1,1

%A _Christian G. Bower_, Jan 04 1999