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A174124 A product triangle sequence:q=1;c(n,q)=If[n == 0, 1, If[n == 1, 1, Product[i*(i + q), {i, 2, n}]]] 1
1, 1, 1, 1, 6, 1, 1, 12, 12, 1, 1, 20, 40, 20, 1, 1, 30, 100, 100, 30, 1, 1, 42, 210, 350, 210, 42, 1, 1, 56, 392, 980, 980, 392, 56, 1, 1, 72, 672, 2352, 3528, 2352, 672, 72, 1, 1, 90, 1080, 5040, 10584, 10584, 5040, 1080, 90, 1, 1, 110, 1650, 9900, 27720, 38808, 27720 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 8, 26, 82, 262, 856, 2858, 9722, 33590, 117570,...}.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..11475

Samuele Giraudo, Tree series and pattern avoidance in syntax trees, arXiv:1903.00677 [math.CO], 2019.

FORMULA

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

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

EXAMPLE

{1},

{1, 1},

{1, 6, 1},

{1, 12, 12, 1},

{1, 20, 40, 20, 1},

{1, 30, 100, 100, 30, 1},

{1, 42, 210, 350, 210, 42, 1},

{1, 56, 392, 980, 980, 392, 56, 1},

{1, 72, 672, 2352, 3528, 2352, 672, 72, 1},

{1, 90, 1080, 5040, 10584, 10584, 5040, 1080, 90, 1},

{1, 110, 1650, 9900, 27720, 38808, 27720, 9900, 1650, 110, 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: A146772 A202868 A202877 * A174345 A174449 A174150

Adjacent sequences:  A174121 A174122 A174123 * A174125 A174126 A174127

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Mar 09 2010

STATUS

approved

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Last modified August 7 17:02 EDT 2020. Contains 336277 sequences. (Running on oeis4.)