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A187259 Number of UH^jU's, DH^jD's, and DH^jU'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). 1

%I

%S 0,0,0,0,0,0,2,11,39,122,358,1008,2770,7493,20049,53239,140603,369837,

%T 969883,2537685,6628215,17288950,45048932,117285552,305159262,

%U 793581817,2062948149,5361112383,13929080271,36183941553,93984332531,244094334682,633922350198,1646271999611

%N Number of UH^jU's, DH^jD's, and DH^jU'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 a(n)=Sum(k*A098056(n,k), k>=0).

%F G.f.=z^5*G^2*(3G-1)(G-1)/[(1-z)(1-z^2*G^2)], where G=1+zG+z^2*G(G-1).

%p eq := g = 1+z*g+z^2*g*(g-1): g := RootOf(eq, g): gser := series(z^5*g^2*(3*g-1)*(g-1)/((1-z)*(1-z^2*g^2)), z = 0, 38): seq(coeff(gser, z, n), n = 0 .. 33);

%Y Cf. A098056, A004148

%K nonn

%O 0,7

%A _Emeric Deutsch_, May 05 2011

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Last modified June 14 15:44 EDT 2021. Contains 345025 sequences. (Running on oeis4.)