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A089899 Square array, read by antidiagonals, where the n-th row is the binomial transform of (1+x+x^2)^n, starting with n=0.

%I A089899 #8 Jun 13 2017 21:49:30
%S A089899 1,1,1,1,2,1,1,3,4,1,1,4,8,7,1,1,5,13,18,11,1,1,6,19,35,36,16,1,1,7,
%T A089899 26,59,83,66,22,1,1,8,34,91,160,179,113,29,1,1,9,43,132,276,392,358,
%U A089899 183,37,1,1,10,53,183,441,752,886,673,283,46,1,1,11,64,245,666,1317,1882,1874
%N A089899 Square array, read by antidiagonals, where the n-th row is the binomial transform of (1+x+x^2)^n, starting with n=0.
%C A089899 Main diagonal is A082759, antidiagonal sums give A052921.
%e A089899 Row 3 = {1,4,13,35,83,179,...} = BINOMIAL({1,3,6,7,6,3,1}).
%e A089899 Rows begin:
%e A089899 [1,1,1,1,1,1,1,1,..],
%e A089899 [1,2,4,7,11,16,22,29,..],
%e A089899 [1,3,8,18,36,66,113,183,..],
%e A089899 [1,4,13,35,83,179,358,673,..],
%e A089899 [1,5,19,59,160,392,886,1874,..],
%e A089899 [1,6,26,91,276,752,1882,4392,..],
%e A089899 [1,7,34,132,441,1317,3599,9143,..],
%e A089899 [1,8,43,183,666,2157,6371,17446,..],..
%o A089899 (PARI) T(n,k)=local(t); if(n<0 || k<0,0, t=sum(j=0,k,binomial(k,j)*polcoeff((1+x+x^2)^n+x*O(x^j),j)))
%Y A089899 Cf. A082759, A052921.
%K A089899 nonn,tabl
%O A089899 0,5
%A A089899 _Paul D. Hanna_, Nov 13 2003