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%I #5 Jun 13 2017 23:36:16
%S 1,1,1,1,3,1,1,11,5,1,1,51,29,7,1,1,291,189,55,9,1,1,1955,1373,463,89,
%T 11,1,1,14947,11037,4159,921,131,13,1,1,127203,97565,39871,9945,1611,
%U 181,15,1,1,1188067,942109,408703,112217,20411,2581,239,17,1
%N Triangle, read by rows, where row n forms a polynomial in y=2*k that generates diagonal n as k=0,1,2,... for n>=0; thus T(n,k) = Sum_{j=0..n-k} T(n-k,j)*(2*k)^j, with T(n,0)=T(n,n)=1.
%e Triangle begins:
%e 1;
%e 1,1;
%e 1,3,1;
%e 1,11,5,1;
%e 1,51,29,7,1;
%e 1,291,189,55,9,1;
%e 1,1955,1373,463,89,11,1;
%e 1,14947,11037,4159,921,131,13,1;
%e 1,127203,97565,39871,9945,1611,181,15,1;
%e 1,1188067,942109,408703,112217,20411,2581,239,17,1; ...
%e where diagonals are generated by row polynomials:
%e T(6,5) = (1) + (1)*(2*5) = 11.
%e T(6,4) = (1) + (3)*(2*4) + (1)*(2*4)^2 = 89.
%e T(6,3) = (1) + (11)*(2*3) + (5)*(2*3)^2 + (1)*(2*3)^3 = 463.
%e T(6,2) = (1) + (51)*(2*2) + (29)*(2*2)^2 + (7)*(2*2)^3 + (1)*(2*2)^4 = 1373.
%o (PARI) T(n,k)=if(n<k || k<0,0,if(n==k || k==0,1,sum(j=0,n-k,T(n-k,j)*(2*k)^j)))
%Y Cf. A091150, A113716, A113712 (column 1), A113713 (column 2), A113714 (column 3), A113715 (row sums).
%K nonn,tabl
%O 0,5
%A _Paul D. Hanna_, Nov 08 2005
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