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A174125 A product triangle sequence:q=2;c(n,q)=If[n == 0, 1, If[n == 1, 1, Product[i*(i + q), {i, 2, n}]]] 0
1, 1, 1, 1, 8, 1, 1, 15, 15, 1, 1, 24, 45, 24, 1, 1, 35, 105, 105, 35, 1, 1, 48, 210, 336, 210, 48, 1, 1, 63, 378, 882, 882, 378, 63, 1, 1, 80, 630, 2016, 2940, 2016, 630, 80, 1, 1, 99, 990, 4158, 8316, 8316, 4158, 990, 99, 1, 1, 120, 1485, 7920, 20790, 28512, 20790 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 10, 32, 95, 282, 854, 2648, 8394, 27128, 89144,...}.

LINKS

Table of n, a(n) for n=0..61.

FORMULA

q=2;c(n,q)=If[n == 0, 1, If[n == 1, 1, Product[i*(i + q), {i, 2, n}]]];

t(n,m,q)=c(n,q)/(c(m,q)*c(n-m,q))

EXAMPLE

{1},

{1, 1},

{1, 8, 1},

{1, 15, 15, 1},

{1, 24, 45, 24, 1},

{1, 35, 105, 105, 35, 1},

{1, 48, 210, 336, 210, 48, 1},

{1, 63, 378, 882, 882, 378, 63, 1},

{1, 80, 630, 2016, 2940, 2016, 630, 80, 1},

{1, 99, 990, 4158, 8316, 8316, 4158, 990, 99, 1},

{1, 120, 1485, 7920, 20790, 28512, 20790, 7920, 1485, 120, 1}

MATHEMATICA

c[n_, q_] = If[n == 0, 1, If[n == 1, 1, Product[i*(i + q), {i, 2, n}]]];

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

Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 1, 2}]

CROSSREFS

Sequence in context: A157170 A143679 A081581 * A051425 A051469 A155494

Adjacent sequences:  A174122 A174123 A174124 * A174126 A174127 A174128

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Mar 09 2010

STATUS

approved

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Last modified August 7 17:44 EDT 2020. Contains 336278 sequences. (Running on oeis4.)