cp's OEIS Frontend

A126191 Triangle read by rows: number of 0-1-2 trees (i.e., ordered trees with vertices of outdegrees 0, 1, or 2) with n edges and exactly k vertices that have 2 children, both being leaves (n >= 0, 0 <= k <= floor((n+2)/4)).

%I A126191 #7 Jul 22 2017 08:35:56
%S A126191 1,1,1,1,3,1,6,3,14,7,33,17,1,79,45,3,194,117,12,482,313,40,1214,843,
%T A126191 129,2,3090,2287,411,10,7936,6247,1278,50,20544,17139,3942,210,53545,
%U A126191 47219,12045,820,5,140399,130527,36559,3052,35,370098,361851,110388
%N A126191 Triangle read by rows: number of 0-1-2 trees (i.e., ordered trees with vertices of outdegrees 0, 1, or 2) with n edges and exactly k vertices that have 2 children, both being leaves (n >= 0, 0 <= k <= floor((n+2)/4)).
%C A126191 Row n has 1 + floor((n+2)/4) terms.
%C A126191 Row sums yield the Motzkin numbers (A001006).
%C A126191 T(n,0) = A025243(n+2) (n >= 1).
%C A126191 Sum_{k=0..floor((n+2)/4)} k*T(n,k) = A002426(n-2) (the central trinomial coefficients).
%F A126191 G.f.: G = G(t,z) satisfies G = 1 + zG + z^2*(G^2 - 1 + t).
%p A126191 G:=(1-z-sqrt(1-2*z-3*z^2+4*z^4-4*z^4*t))/2/z^2: Gser:=simplify(series(G,z=0,21)): for n from 0 to 17 do P[n]:=sort(coeff(Gser,z,n)) od: for n from 0 to 17 do seq(coeff(P[n],t,j),j=0..floor((n+2)/4)) od; # yields sequence in triangular form
%Y A126191 Cf. A001006, A002426, A025243.
%K A126191 nonn,tabf
%O A126191 0,5
%A A126191 _Emeric Deutsch_, Dec 27 2006