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A174449 A symmetrical triangle sequence:q=1;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, 6, 1, 1, 12, 12, 1, 1, 20, 240, 20, 1, 1, 30, 600, 600, 30, 1, 1, 42, 1260, 25200, 1260, 42, 1, 1, 56, 2352, 70560, 70560, 2352, 56, 1, 1, 72, 4032, 169344, 5080320, 169344, 4032, 72, 1, 1, 90, 6480, 362880, 15240960, 15240960, 362880, 6480, 90, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 8, 26, 282, 1262, 27806, 145938, 5427218, 31220822, 1757784822,...}.

LINKS

Table of n, a(n) for n=0..55.

FORMULA

q=1;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, 6, 1},

{1, 12, 12, 1},

{1, 20, 240, 20, 1},

{1, 30, 600, 600, 30, 1},

{1, 42, 1260, 25200, 1260, 42, 1},

{1, 56, 2352, 70560, 70560, 2352, 56, 1},

{1, 72, 4032, 169344, 5080320, 169344, 4032, 72, 1},

{1, 90, 6480, 362880, 15240960, 15240960, 362880, 6480, 90, 1},

{1, 110, 9900, 712800, 39916800, 1676505600, 39916800, 712800, 9900, 110, 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: A202877 A174124 A174345 * A174150 A202673 A202875

Adjacent sequences:  A174446 A174447 A174448 * A174450 A174451 A174452

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Mar 20 2010

STATUS

approved

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Last modified September 28 20:03 EDT 2021. Contains 347717 sequences. (Running on oeis4.)