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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
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, 945, 63, 1, 1, 84, 1764, 13230, 13230, 1764, 84, 1, 1, 108, 3024, 31752, 142884, 31752, 3024, 108, 1, 1, 135, 4860, 68040, 428652, 428652, 68040, 4860, 135, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

The sequence is based on Narayana numbers.

Row sums are:

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

LINKS

Table of n, a(n) for n=1..55.

FORMULA

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)]

EXAMPLE

{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, 945, 63, 1},

{1, 84, 1764, 13230, 13230, 1764, 84, 1},

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

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

MATHEMATICA

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}];

Flatten[%]

CROSSREFS

Cf. A081582

Sequence in context: A168625 A143681 A081582 * A144404 A014761 A073702

Adjacent sequences:  A174343 A174344 A174345 * A174347 A174348 A174349

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Mar 16 2010

STATUS

approved

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Last modified August 20 23:38 EDT 2019. Contains 326155 sequences. (Running on oeis4.)