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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
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, 30, 1, 1, 42, 630, 2100, 2100, 630, 42, 1, 1, 56, 1176, 5880, 9800, 5880, 1176, 56, 1, 1, 72, 2016, 14112, 35280, 35280, 14112, 2016, 72, 1, 1, 90, 3240, 30240, 105840, 158760 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

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

LINKS

Table of n, a(n) for n=0..60.

FORMULA

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))

EXAMPLE

{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, 30, 1},

{1, 42, 630, 2100, 2100, 630, 42, 1},

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

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

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

MATHEMATICA

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]);

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

Flatten[%]

CROSSREFS

Sequence in context: A155864 A145903 A223257 * A329228 A172373 A174411

Adjacent sequences:  A173878 A173879 A173880 * A173882 A173883 A173884

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Mar 01 2010

STATUS

approved

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Last modified July 5 00:01 EDT 2020. Contains 335457 sequences. (Running on oeis4.)