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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 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.)