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A156006 A symmetrical triangle based on A009799: a(n,m) = -(m - n)/(m + n)*Binomial[n + m, n]; t(n,m) = If[n == 0, 1, a(n, m) + a(n, n - m)] 0

%I

%S 1,1,1,1,2,1,1,4,4,1,1,8,10,8,1,1,18,23,23,18,1,1,47,56,56,56,47,1,1,

%T 138,152,138,138,152,138,1,1,436,456,372,330,372,456,436,1,1,1438,

%U 1465,1111,847,847,1111,1465,1438,1,1,4871,4906,3586,2431,2002,2431,3586

%N A symmetrical triangle based on A009799: a(n,m) = -(m - n)/(m + n)*Binomial[n + m, n]; t(n,m) = If[n == 0, 1, a(n, m) + a(n, n - m)]

%C Row sums are:

%C {1, 2, 4, 10, 28, 84, 264, 858, 2860, 9724, 33592,...}.

%F a(n,m) = -(m - n)/(m + n)*Binomial[n + m, n];

%F t(n,m) = If[n == 0, 1, a(n, m) + a(n, n - m)]

%e {1},

%e {1, 1},

%e {1, 2, 1},

%e {1, 4, 4, 1},

%e {1, 8, 10, 8, 1},

%e {1, 18, 23, 23, 18, 1},

%e {1, 47, 56, 56, 56, 47, 1},

%e {1, 138, 152, 138, 138, 152, 138, 1},

%e {1, 436, 456, 372, 330, 372, 456, 436, 1},

%e {1, 1438, 1465, 1111, 847, 847, 1111, 1465, 1438, 1},

%e {1, 4871, 4906, 3586, 2431, 2002, 2431, 3586, 4906, 4871, 1}

%t a[n_, m_] = -(m - n)/(m + n)*Binomial[n + m, n];

%t t[n_, m_] = If[n == 0, 1, a[n, m] + a[n, n - m]];

%t Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

%t Flatten[%]

%Y A009799

%K nonn,tabl,uned

%O 0,5

%A _Roger L. Bagula_, Feb 01 2009

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Last modified July 21 21:14 EDT 2019. Contains 325199 sequences. (Running on oeis4.)