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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 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.)