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A104730 Triangle read by rows: T(n,k)=C(n+1,k)-C(k,n-k+1).

%I A104730 #9 Jan 16 2024 14:25:00
%S A104730 1,1,1,1,3,1,1,4,5,1,1,5,10,7,1,1,6,15,19,9,1,1,7,21,35,31,11,1,1,8,
%T A104730 28,56,69,46,13,1,1,9,36,84,126,121,64,15,1,1,10,45,120,210,251,195,
%U A104730 85,17,1,1,11,55,165,330,462,456,295,109,19,1,1,12,66
%N A104730 Triangle read by rows: T(n,k)=C(n+1,k)-C(k,n-k+1).
%C A104730 Row sums are A027934: 1, 2, 5, 11, 24, 51, 107... Diagonal sums are A131298.
%H A104730 Harvey P. Dale, <a href="/A104730/b104730.txt">Table of n, a(n) for n = 1..1000</a>
%F A104730 Perform the operation A - B; then extract the triangle after deleting all zeros. P = infinite lower triangular Pascal's triangle matrix (A007318); B = A026729, as an infinite lower triangular matrix: [1; 0, 1;, 0, 1, 1; 0, 0, 2, 1; 0, 0, 1, 3, 1;...].
%e A104730 The first few rows of the triangle are:
%e A104730 1;
%e A104730 1, 1;
%e A104730 1, 3, 1;
%e A104730 1, 4, 5, 1;
%e A104730 1, 5, 10, 7, 1;
%e A104730 1, 6, 15, 19, 9, 1;
%e A104730 1, 7, 31, 35, 31, 11, 1;
%e A104730 ...
%t A104730 Table[Binomial[n+1,k]-Binomial[k,n-k+1],{n,0,20},{k,0,n}]//Flatten (* _Harvey P. Dale_, Jan 16 2024 *)
%Y A104730 Cf. A027934, A026729, A007318.
%K A104730 nonn,tabl
%O A104730 1,5
%A A104730 _Gary W. Adamson_, Mar 20 2005
%E A104730 Better definition from _Paul Barry_, Jun 26 2007
%E A104730 More terms from _Harvey P. Dale_, Jan 16 2024