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A174126 A product triangle sequence:c(n)=If[n == 0, 1, If[n == 1, 1, Product[i^2 - 2*i + 1, {i, 2, n}]]] 0
1, 1, 1, 1, 1, 1, 1, 4, 4, 1, 1, 9, 36, 9, 1, 1, 16, 144, 144, 16, 1, 1, 25, 400, 900, 400, 25, 1, 1, 36, 900, 3600, 3600, 900, 36, 1, 1, 49, 1764, 11025, 19600, 11025, 1764, 49, 1, 1, 64, 3136, 28224, 78400, 78400, 28224, 3136, 64, 1, 1, 81, 5184, 63504, 254016, 396900 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Row sums are:

{1, 2, 3, 10, 56, 322, 1752, 9074, 45278, 219650, 1042472,...}.

LINKS

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

FORMULA

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

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

EXAMPLE

{1},

{1, 1},

{1, 1, 1},

{1, 4, 4, 1},

{1, 9, 36, 9, 1},

{1, 16, 144, 144, 16, 1},

{1, 25, 400, 900, 400, 25, 1},

{1, 36, 900, 3600, 3600, 900, 36, 1},

{1, 49, 1764, 11025, 19600, 11025, 1764, 49, 1},

{1, 64, 3136, 28224, 78400, 78400, 28224, 3136, 64, 1},

{1, 81, 5184, 63504, 254016, 396900, 254016, 63504, 5184, 81, 1}

MATHEMATICA

c[n_] = If[n == 0, 1, If[n == 1, 1, Product[i^2 - 2*i + 1, {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: A198929 A172347 A108428 * A075613 A221837 A189150

Adjacent sequences:  A174123 A174124 A174125 * A174127 A174128 A174129

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.)