%I A140182
%S A140182 1,2,3,3,7,1,4,12,4,3,5,18,10,13,1,6,25,20,35,6,3,7,33,35,75,21,19,1,8,
%T A140182 42,56,140,56,70,8,3,9,52,84,238,126,196,36,25,1,10,63,120,378,252,462,
%U A140182 120,117,10,3,11,75,165,570,462,966,330,405,55,31,1
%N A140182 Binomial transform of an infinite bidiagonal matrix with (1,3,1,3,1,3,
               ...) in the main diagonal, (1,1,1,...) in the subdiagonal, the rest 
               zeros.
%C A140182 Row sums = A052940: (1, 5, 11, 23, 47, 95,...).
%F A140182 A007318 as an infinite lower triangular matrix * a bidiagonal matrix 
               with (1,3,1,3,1,3,...) in the main diagonal, (1,1,1,...) in the subdiagonal 
               and the rest zeros.
%F A140182 T(n,2k)=binom(n+1,2k+1); T(n,2k+1)=2*binom(n,2k+1)+binom(n+1,2k+2). - 
               Emeric Deutsch (deutsch(AT)duke.poly.edu), May 18 2008
%e A140182 First few rows of the triangle are:
%e A140182 1;
%e A140182 2, 3;
%e A140182 3, 7, 1;
%e A140182 4, 12, 4, 3;
%e A140182 5, 18, 10, 13, 1;
%e A140182 6, 25, 20, 35, 6, 3;
%e A140182 7, 33, 35, 75 21, 19, 1;
%e A140182 ...
%p A140182 T:=proc(n,k) if `mod`(k,2)=0 then binomial(n+1,k+1) else 2*binomial(n,
               k)+binomial(n+1,k+1) end if end proc: for n from 0 to 10 do seq(T(n,
               k),k=0..n) end do; # yields sequence in triangular form - Emeric 
               Deutsch (deutsch(AT)duke.poly.edu), May 18 2008
%Y A140182 Cf. A052940.
%Y A140182 Sequence in context: A028257 A100228 A111003 this_sequence A082910 A023646 
               A056225
%Y A140182 Adjacent sequences: A140179 A140180 A140181 this_sequence A140183 A140184 
               A140185
%K A140182 nonn,tabl
%O A140182 0,2
%A A140182 Gary W. Adamson (qntmpkt(AT)yahoo.com), May 11 2008