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A174345 A symmetrical triangle sequence:t(n,m)=(Binomial[n - 1, m - 1]*Binomial[ n, m - 1]/m)*If[Floor[n/2] greater than or equal to , 2^(m - 1), 2^(n - m)] 0

%I

%S 1,1,1,1,6,1,1,12,12,1,1,20,80,20,1,1,30,200,200,30,1,1,42,420,1400,

%T 420,42,1,1,56,784,3920,3920,784,56,1,1,72,1344,9408,28224,9408,1344,

%U 72,1,1,90,2160,20160,84672,84672,20160,2160,90,1

%N A symmetrical triangle sequence:t(n,m)=(Binomial[n - 1, m - 1]*Binomial[ n, m - 1]/m)*If[Floor[n/2] greater than or equal to , 2^(m - 1), 2^(n - m)]

%C The sequence is based on Narayana numbers.

%C Row sums are:

%C {1, 3, 9, 39, 143, 693, 2789, 14283, 60699, 321249,...}.

%F t(n,m)=(Binomial[n - 1, m - 1]*Binomial[ n, m - 1]/m)*If[Floor[n/2] greater than or equal to , 2^(m - 1), 2^(n - m)]

%e {1},

%e {1, 1},

%e {1, 6, 1},

%e {1, 12, 12, 1},

%e {1, 20, 80, 20, 1},

%e {1, 30, 200, 200, 30, 1},

%e {1, 42, 420, 1400, 420, 42, 1},

%e {1, 56, 784, 3920, 3920, 784, 56, 1},

%e {1, 72, 1344, 9408, 28224, 9408, 1344, 72, 1},

%e {1, 90, 2160, 20160, 84672, 84672, 20160, 2160, 90, 1}

%t Table[Table[(Binomial[n - 1, m - 1]*Binomial[n, m - 1]/m)* If[Floor[n/2] >= m, 2^(m - 1), 2^(n - m)], {m, 1, n}], {n, 1, 10}];

%t Flatten[%]

%K nonn,tabl,uned

%O 1,5

%A _Roger L. Bagula_, Mar 16 2010

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Last modified September 26 20:34 EDT 2021. Contains 347672 sequences. (Running on oeis4.)