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A174346 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 , 3^(m - 1), 3^(n - m)] 0

%I

%S 1,1,1,1,9,1,1,18,18,1,1,30,180,30,1,1,45,450,450,45,1,1,63,945,4725,

%T 945,63,1,1,84,1764,13230,13230,1764,84,1,1,108,3024,31752,142884,

%U 31752,3024,108,1,1,135,4860,68040,428652,428652,68040,4860,135,1

%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 , 3^(m - 1), 3^(n - m)]

%C The sequence is based on Narayana numbers.

%C Row sums are:

%C {1, 2, 11, 38, 242, 992, 6743, 30158, 212654, 1003376,...}.

%F t(n,m)=(Binomial[n - 1, m - 1]*Binomial[ n, m - 1]/m)*If[Floor[n/2] greater than or equal to , 3^(m - 1), 3^(n - m)]

%e {1},

%e {1, 1},

%e {1, 9, 1},

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

%e {1, 30, 180, 30, 1},

%e {1, 45, 450, 450, 45, 1},

%e {1, 63, 945, 4725, 945, 63, 1},

%e {1, 84, 1764, 13230, 13230, 1764, 84, 1},

%e {1, 108, 3024, 31752, 142884, 31752, 3024, 108, 1},

%e {1, 135, 4860, 68040, 428652, 428652, 68040, 4860, 135, 1}

%t Table[Table[(Binomial[n - 1, m - 1]*Binomial[n, m - 1]/m)* If[Floor[n/2] >= m, 3^(m - 1), 3^(n - m)], {m, 1, n}], {n, 1, 10}];

%t Flatten[%]

%Y Cf. A081582

%K nonn,tabl,uned

%O 1,5

%A _Roger L. Bagula_, Mar 16 2010

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Last modified September 26 17:00 EDT 2021. Contains 347670 sequences. (Running on oeis4.)