cp's OEIS Frontend

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.

%I A140182 #8 Jul 21 2019 17:19:33
%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,
%T A140182 8,42,56,140,56,70,8,3,9,52,84,238,126,196,36,25,1,10,63,120,378,252,
%U A140182 462,120,117,10,3,11,75,165,570,462,966,330,405,55,31,1
%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 From _Emeric Deutsch_, May 18 2008: (Start)
%F A140182 T(n, 2k) = binomial(n+1, 2k+1);
%F A140182 T(n, 2k+1) = 2*binomial(n, 2k+1) + binomial(n+1, 2k+2). (End)
%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_, May 18 2008
%Y A140182 Cf. A052940.
%K A140182 nonn,tabl
%O A140182 0,2
%A A140182 _Gary W. Adamson_, May 11 2008