%I A138767
%S A138767 1,1,4,4,15,18,3,56,80,24,210,350,150,10,792,1512,840,120,3003,6468,
%T A138767 4410,980,35,11440,27456,22176,6720,560,43758,115830,108108,41580,5670,
%U A138767 126,167960,486200,514800,240240,46200,2520
%N A138767 Triangle read by rows: T(n,k)=binom(n,k)*binom(2*n-2*k,n-1), n>=1, 0<=k<=floor(n/
               2+1/2).
%C A138767 Row n contains floor(n/2+3/2) terms.
%C A138767 Row sums with alternate signs are 0.
%D A138767 D. Beckwith, Problem 11212/11220, Amer. Math. Monthly 115, (2008), p. 
               366.
%e A138767 Triangle starts:
%e A138767 1,1;
%e A138767 4,4;
%e A138767 15,18,3;
%e A138767 56,18,3;
%e A138767 210,350,150,10;
%p A138767 T:=proc(n,r) options operator, arrow: binomial(n,r)*binomial(2*n-2*r,
               n-1) end proc: for n to 10 do seq(T(n,k),k=0..floor((1/2)*n+1/2)) 
               end do; # yields sequence in triangular form
%Y A138767 Sequence in context: A059443 A097335 A117187 this_sequence A048282 A068592 
               A135944
%Y A138767 Adjacent sequences: A138764 A138765 A138766 this_sequence A138768 A138769 
               A138770
%K A138767 nonn,tabf
%O A138767 1,3
%A A138767 Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2008