%I #33 Oct 20 2019 02:10:06
%S 1,2,2,4,8,16,33,56,90,164,330,688,1440,3008,6291,13168,27604,57896,
%T 120730,248312,501464,995664,1954582,3821328,7495996,14848472,
%U 29815976,60741680,125363472,261452256,549461078,1160693056,2459679936,5221717888
%N Number of black-rooted red-black trees with n internal nodes.
%H Alois P. Heinz, <a href="/A001137/b001137.txt">Table of n, a(n) for n = 1..900</a>
%H F. Ruskey, <a href="https://webhome.cs.uvic.ca/~cos/inf/tree/RedBlackTree.html">Information on Red-Black Trees</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Red-BlackTree.html">Red-Black Tree.</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F G.f. satisfies: A(x) = x*(1+x)^2*(1 + A((x+x^2)^2)). - _Paul D. Hanna_, Jun 14 2012
%t m = 35; A[_] = 0;
%t Do[A[x_] = x*(1 + x)^2*(1 + A[(x + x^2)^2]) + O[x]^m // Normal, {m}];
%t CoefficientList[A[x]/x, x] (* _Jean-François Alcover_, Oct 19 2019 *)
%o (PARI) {a(n)=local(A=x);for(i=1,n,A=x*(1+x)^2*(1 + subst(A,x,(x+x^2)^2+x*O(x^n))));polcoeff(A,n)} \\ _Paul D. Hanna_, Jun 14 2012
%Y Cf. A001131.
%K nonn
%O 1,2
%A _Frank Ruskey_
%E More terms from _Sean A. Irvine_, Mar 08 2012