%I A112308
%S A112308 1,6,25,93,333,1180,4183,14895,53349,192239,696765,2539157,9299547,
%T A112308 34215102,126411177,468822297,1744799967,6514363557,24393558687,
%U A112308 91591471287,344764147407,1300756937445,4918188617379,18633066901747
%N A112308 Sum of the heights of the second peaks in all Dyck paths of semilength 
               n+2.
%C A112308 a(n)=sum(k*A112307(n+2,k), k=0..n+1).
%F A112308 G.f.=c^4*(1+zc)/(1-z), where c=[1-sqrt(1-4z)]/(2z) is the Catalan function.
%e A112308 a(1)=6 because the second peaks of the Dyck paths UDUDUD, UDUUDD, UUDDUD, 
               UUDUDD and UUUDDD, where U=(1,1), D=(1,-1), are 1, 2, 1, 2 and 0, 
               respectively.
%p A112308 c:=(1-sqrt(1-4*z))/2/z: g:=series(c^4*(1+z*c)/(1-z),z=0,32): 1,seq(coeff(g,
               z^n),n=1..27);
%Y A112308 Cf. A112307.
%Y A112308 Sequence in context: A099948 A143815 A092491 this_sequence A034336 A092184 
               A034559
%Y A112308 Adjacent sequences: A112305 A112306 A112307 this_sequence A112309 A112310 
               A112311
%K A112308 nonn
%O A112308 0,2
%A A112308 Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 30 2005