# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a038077 Showing 1-1 of 1 %I A038077 #24 Mar 01 2016 03:15:38 %S A038077 2,4,10,36,132,532,2222,9584,42248,189776,864830,3989656,18593424, %T A038077 87413444,414060796,1974260912,9467922870,45638482068,221001289714, %U A038077 1074591477112,5244497440468,25681907242416,126149132242490,621386729646752,3068748094479108 %N A038077 Number of rooted identity trees with 2-colored nodes. %C A038077 Shifts left and halves under Weigh transform. %H A038077 Alois P. Heinz, Table of n, a(n) for n = 1..500 %H A038077 N. J. A. Sloane, Transforms %H A038077 Index entries for sequences related to rooted trees %F A038077 a(n) = 2 * A005753(n). %p A038077 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, %p A038077 add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i))) %p A038077 end: %p A038077 a:= n-> `if`(n=1, 2, 2*b((n-1)$2)): %p A038077 seq(a(n), n=1..40); # _Alois P. Heinz_, May 20 2013 %t A038077 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 A038077 a[n_] := If[n==1, 2, 2*b[n-1, n-1]]; %t A038077 Table[a[n], {n, 1, 40}] (* _Jean-François Alcover_, Mar 01 2016, after _Alois P. Heinz_ *) %Y A038077 Cf. A004111, A038078, A038079, A038080, A246312. %K A038077 nonn,eigen %O A038077 1,1 %A A038077 _Christian G. Bower_, Jan 04 1999 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE