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Triangle sequence: t(n,m)=(n+1)*(n+m)!.
0

%I #2 Oct 12 2012 14:54:52

%S 1,2,4,6,18,72,24,96,480,2880,120,600,3600,25200,201600,720,4320,

%T 30240,241920,2177280,21772800,5040,35280,282240,2540160,25401600,

%U 279417600,3353011200,40320,322560,2903040,29030400,319334400,3832012800

%N Triangle sequence: t(n,m)=(n+1)*(n+m)!.

%C Row sums are:

%C {1, 6, 96, 3480, 231120, 24227280, 3660693120, 751426139520, 200919532665600, 67803855263020800, 28174602435225523200}.

%F t(n,m)=(n+1)*(n+m)!.

%e {1},

%e {2, 4},

%e {6, 18, 72},

%e {24, 96, 480, 2880},

%e {120, 600, 3600, 25200, 201600},

%e {720, 4320, 30240, 241920, 2177280, 21772800},

%e {5040, 35280, 282240, 2540160, 25401600, 279417600, 3353011200},

%e {40320, 322560, 2903040, 29030400, 319334400, 3832012800, 49816166400, 697426329600},

%e {362880, 3265920, 32659200, 359251200, 4311014400, 56043187200, 784604620800, 11769069312000, 188305108992000},

%e {3628800, 36288000, 399168000, 4790016000, 62270208000, 871782912000, 13076743680000, 209227898880000, 3556874280960000, 64023737057280000}, {39916800, 439084800, 5269017600, 68497228800, 958961203200, 14384418048000, 230150688768000, 3912561709056000, 70426110763008000, 1338096104497152000, 26761922089943040000}

%t Clear[t, n, m]; t[n_, m_] := (n+1)*(n + m)!; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]

%K nonn,uned

%O 1,2

%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 16 2008