%I
%S 0,0,0,1,3,7,17,41,99,242,596,1477,3681,9215,23155,58368,147530,
%T 373768,948882,2413264,6147414,15682008,40056238,102434119,262228051,
%U 671945055,1723350315,4423518544,11362907022,29208834520,75131251334,193370093508,497969663062
%N Number of UH^jD's for some j>0, in all peakless Motzkin paths of length n (here U=(1,1), D=(1,1) and H=(1,0); can be easily expressed using RNA secondary structure terminology).
%C Same as A089742 except for the first three terms.  _Georg Fischer_, Oct 14 2018
%F G.f.: z^3*G^2/((1z)*(1z^2*G^2)), where G = 1+z*G+z^2*G*(G1).
%F a(n) = Sum_{k>=0} k*A089741(n,k).
%e a(4)=3 because in HHHH, HUHD, UHDH and UHHD we have 0+1+1+1 subwords of the type UH^jD.
%p eq := g = 1+z*g+z^2*g*(g1): G := RootOf(eq, g): Gser := series(z^3*G^2/((1z)*(1z^2*G^2)), z = 0, 35): seq(coeff(Gser, z, n), n = 0 .. 32);
%Y Cf. A004148, A089741, A089742.
%K nonn
%O 0,5
%A _Emeric Deutsch_, May 05 2011
