Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #4 Sep 08 2013 13:31:05
%S 1,3,1,5,9,1,7,30,18,1,9,70,100,30,1,11,135,350,250,45,1,13,231,945,
%T 1225,525,63,1,15,364,2156,4410,3430,980,84,1,17,540,4368,12936,15876,
%U 8232,1680,108,1,19,765,8100,32760,58212,47628,17640,2700,135,1
%N Triangle T(n,k), 1<=k<=n, read by rows defined by :T(n,k)=C(n,k)*C(n-1,k-1)+C(n,k-1)*C(n-1,k)where C(n,k)=A007318(n,k) .
%F T(n,k)=A001263(n,k)*(2n-2k+1). Sum_{k, 1<=k<=n}T(n,k)=binomial(2n,n-1)=A001791(n). T(2n-1,n)=A060150(n), n>=1 .
%e Triangle begins:
%e 1;
%e 3, 1;
%e 5, 9, 1;
%e 7, 30, 18, 1;
%e 9, 70, 100, 30, 1;
%e 11, 135, 350, 250, 45, 1;
%e 13, 231, 945, 1225, 525, 63, 1;
%e 15, 364, 2156, 4410, 3430, 980, 84, 1 ;...
%Y Cf. A005408, A002414.
%K nonn,tabl
%O 1,2
%A _Philippe Deléham_, Apr 11 2007