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A084867 Symmetric square table, read by antidiagonals, such that antidiagonal sums form the first row shifted left: T(0,0)=1, T(0,k) = Sum_{m=0..k-1} T(m,k-1-m) when k > 0; and T(n,k) = T(n-1,k) + T(n,k-1) when n > 0, k > 0.

%I A084867 #10 Nov 19 2017 01:41:32
%S A084867 1,1,1,2,2,2,6,4,4,6,20,10,8,10,20,68,30,18,18,30,68,232,98,48,36,48,
%T A084867 98,232,792,330,146,84,84,146,330,792,2704,1122,476,230,168,230,476,
%U A084867 1122,2704,9232,3826,1598,706,398,398,706,1598,3826,9232,31520,13058,5424
%N A084867 Symmetric square table, read by antidiagonals, such that antidiagonal sums form the first row shifted left: T(0,0)=1, T(0,k) = Sum_{m=0..k-1} T(m,k-1-m) when k > 0; and T(n,k) = T(n-1,k) + T(n,k-1) when n > 0, k > 0.
%C A084867 Antidiagonal sums give A006012. Table is symmetric under transpose, so that first column equals the first row. Second row gives partial sums of first row.
%F A084867 T(0,0)=1, T(0,1)=1, T(0,n) = 4*T(0,n-1) - 2*T(0,n-2) when n >= 2.
%e A084867 Table begins:
%e A084867      1,     1,     2,     6,    20,    68,   232,    792, ...
%e A084867      1,     2,     4,    10,    30,    98,   330,   1122, ...
%e A084867      2,     4,     8,    18,    48,   146,   476,   1598, ...
%e A084867      6,    10,    18,    36,    84,   230,   706,   2304, ...
%e A084867     20,    30,    48,    84,   168,   398,  1104,   3408, ...
%e A084867     68,    98,   146,   230,   398,   796,  1900,   5308, ...
%e A084867    232,   330,   476,   706,  1104,  1900,  3800,   9108, ...
%e A084867    792,  1122,  1598,  2304,  3408,  5308,  9108,  18216, ...
%e A084867   2704,  3826,  5424,  7728, 11136, 16444, 25552,  43768, ...
%e A084867   9232, 13058, 18482, 26210, 37346, 53790, 79342, 123110, ...
%Y A084867 Cf. A006012 (row sums), A084868 (main diagonal).
%K A084867 nonn,tabl
%O A084867 0,4
%A A084867 _Paul D. Hanna_, Jun 10 2003, Jun 11 2003