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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

%I

%S 1,1,1,1,6,1,1,12,12,1,1,20,240,20,1,1,30,600,600,30,1,1,42,1260,

%T 25200,1260,42,1,1,56,2352,70560,70560,2352,56,1,1,72,4032,169344,

%U 5080320,169344,4032,72,1,1,90,6480,362880,15240960,15240960,362880,6480,90,1,1

%N 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)!)]

%C Row sums are:

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

%F 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)!)]

%e {1},

%e {1, 1},

%e {1, 6, 1},

%e {1, 12, 12, 1},

%e {1, 20, 240, 20, 1},

%e {1, 30, 600, 600, 30, 1},

%e {1, 42, 1260, 25200, 1260, 42, 1},

%e {1, 56, 2352, 70560, 70560, 2352, 56, 1},

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

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

%e {1, 110, 9900, 712800, 39916800, 1676505600, 39916800, 712800, 9900, 110, 1}

%t 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}]

%K nonn,tabl,uned

%O 0,5

%A _Roger L. Bagula_, Mar 20 2010

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Last modified October 20 12:43 EDT 2021. Contains 348108 sequences. (Running on oeis4.)