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A174450 A symmetrical triangle sequence:q=2;t(n,m,q)=If[Floor[n/2] greater than or equal to m, n!*(n + 1)!* q^m/((n - m)!(n - m + 1)!), n!*(n + 1)!*q^(n - m)/(m!*(m + 1)!)] 0
1, 1, 1, 1, 12, 1, 1, 24, 24, 1, 1, 40, 960, 40, 1, 1, 60, 2400, 2400, 60, 1, 1, 84, 5040, 201600, 5040, 84, 1, 1, 112, 9408, 564480, 564480, 9408, 112, 1, 1, 144, 16128, 1354752, 81285120, 1354752, 16128, 144, 1, 1, 180, 25920, 2903040, 243855360 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 14, 50, 1042, 4922, 211850, 1148002, 84027170, 493569002, 54937001242,...}.

LINKS

Table of n, a(n) for n=0..49.

FORMULA

q=2;t(n,m,q)=If[Floor[n/2] greater than or equal to m, n!*(n + 1)!* q^m/((n - m)!(n - m + 1)!), n!*(n + 1)!*q^(n - m)/(m!*(m + 1)!)]

EXAMPLE

{1},

{1, 1},

{1, 12, 1},

{1, 24, 24, 1},

{1, 40, 960, 40, 1},

{1, 60, 2400, 2400, 60, 1},

{1, 84, 5040, 201600, 5040, 84, 1},

{1, 112, 9408, 564480, 564480, 9408, 112, 1},

{1, 144, 16128, 1354752, 81285120, 1354752, 16128, 144, 1},

{1, 180, 25920, 2903040, 243855360, 243855360, 2903040, 25920, 180, 1},

{1, 220, 39600, 5702400, 638668800, 53648179200, 638668800, 5702400, 39600, 220, 1}

MATHEMATICA

Table[Flatten[Table[Table[If[Floor[n/2] >= m, n!*(n + 1)!*q^m/((n - m)!(n - m + 1)!), n!*( n + 1)!*q^(n - m)/(m!*(m + 1)!)], {m, 0, n}], {n, 0, 10}]], {q, 1, 10}]

CROSSREFS

Sequence in context: A070636 A168646 A051457 * A166343 A186432 A176489

Adjacent sequences:  A174447 A174448 A174449 * A174451 A174452 A174453

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Mar 20 2010

STATUS

approved

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Last modified October 18 15:41 EDT 2021. Contains 348068 sequences. (Running on oeis4.)