%I A127534
%S A127534 0,1,9,65,442,2940,19380,127281,834900,5476185,35937525,236030652,
%T A127534 1551652424,10210456360,67254204696,443410005585,2926078447656,
%U A127534 19325957314755,127746785056275,845069382939705,5594334252541650
%N A127534 Number of jumps in all even trees with 2n edges. An even tree is an ordered 
               tree in which each vertex has an even outdegree. In the preorder 
               traversal of an ordered tree, any transition from a node at a deeper 
               level to a node on a strictly higher level is called a jump.
%C A127534 The Krandick reference considers jumps in full binary trees.
%D A127534 W. Krandick, Trees and jumps and real roots, J. Computational and Applied 
               Math., 162, 2004, 51-55.
%F A127534 a(n)=(n-1)(4n-3)C(3n,n)/[3(2n+1)(3n-1)].
%p A127534 seq((n-1)*(4*n-3)*binomial(3*n,n)/3/(2*n+1)/(3*n-1),n=1..24);
%Y A127534 Cf. A127535, A127536.
%Y A127534 Sequence in context: A055284 A081040 A102902 this_sequence A037548 A036731 
               A020234
%Y A127534 Adjacent sequences: A127531 A127532 A127533 this_sequence A127535 A127536 
               A127537
%K A127534 nonn
%O A127534 1,3
%A A127534 Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 19 2007