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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
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, 420, 42, 1, 1, 56, 784, 3920, 3920, 784, 56, 1, 1, 72, 1344, 9408, 28224, 9408, 1344, 72, 1, 1, 90, 2160, 20160, 84672, 84672, 20160, 2160, 90, 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, 3, 9, 39, 143, 693, 2789, 14283, 60699, 321249,...}.

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 , 2^(m - 1), 2^(n - m)]

EXAMPLE

{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, 420, 42, 1},

{1, 56, 784, 3920, 3920, 784, 56, 1},

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

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

MATHEMATICA

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}];

Flatten[%]

CROSSREFS

Sequence in context: A202868 A202877 A174124 * A174449 A174150 A202673

Adjacent sequences:  A174342 A174343 A174344 * A174346 A174347 A174348

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Mar 16 2010

STATUS

approved

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Last modified July 29 17:41 EDT 2021. Contains 346346 sequences. (Running on oeis4.)