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A173881 Double product triangle:c(n)=If[n == 1, 1, If[n == 0, 1, Product[(i - 1)*i, {i, 2, n}]]];t(n,m)=c(n)/(c(m)*c(n-m)) 0

%I

%S 1,1,1,1,2,1,1,6,6,1,1,12,36,12,1,1,20,120,120,20,1,1,30,300,600,300,

%T 30,1,1,42,630,2100,2100,630,42,1,1,56,1176,5880,9800,5880,1176,56,1,

%U 1,72,2016,14112,35280,35280,14112,2016,72,1,1,90,3240,30240,105840,158760

%N Double product triangle:c(n)=If[n == 1, 1, If[n == 0, 1, Product[(i - 1)*i, {i, 2, n}]]];t(n,m)=c(n)/(c(m)*c(n-m))

%C Row sums are:

%C {1, 2, 4, 14, 62, 282, 1262, 5546, 24026, 102962, 437582,...}.

%F c(n)=If[n == 1, 1, If[n == 0, 1, Product[(i - 1)*i, {i, 2, n}]]];

%F t(n,m)=c(n)/(c(m)*c(n-m))

%e {1},

%e {1, 1},

%e {1, 2, 1},

%e {1, 6, 6, 1},

%e {1, 12, 36, 12, 1},

%e {1, 20, 120, 120, 20, 1},

%e {1, 30, 300, 600, 300, 30, 1},

%e {1, 42, 630, 2100, 2100, 630, 42, 1},

%e {1, 56, 1176, 5880, 9800, 5880, 1176, 56, 1},

%e {1, 72, 2016, 14112, 35280, 35280, 14112, 2016, 72, 1},

%e {1, 90, 3240, 30240, 105840, 158760, 105840, 30240, 3240, 90, 1}

%t c[n_] = If[n == 1, 1, If[n == 0, 1, Product[(i - 1)*i, {i, 2, n}]]];

%t t[n_, m_] = c[n]/(c[m]*c[n - m]);

%t Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

%t Flatten[%]

%K nonn,tabl,uned

%O 0,5

%A _Roger L. Bagula_, Mar 01 2010

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Last modified August 4 08:25 EDT 2020. Contains 336201 sequences. (Running on oeis4.)