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 A174127 A product triangle sequence:q=3;c(n,q)=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, 8, 8, 1, 1, 27, 216, 27, 1, 1, 64, 1728, 1728, 64, 1, 1, 125, 8000, 27000, 8000, 125, 1, 1, 216, 27000, 216000, 216000, 27000, 216, 1, 1, 343, 74088, 1157625, 2744000, 1157625, 74088, 343, 1, 1, 512, 175616, 4741632, 21952000, 21952000 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Row sums are: {1, 2, 3, 18, 272, 3586, 43252, 486434, 5208114, 53739522, 538849100,...}. LINKS FORMULA q=3:c(n,q)=If[n == 0, 1, If[n == 1, 1, Product[(i-1)^q, {i, 2, n}]]]; t(n,m,q)=c(n,q)/(c(m,q)*c(n-m,q)) EXAMPLE {1}, {1, 1}, {1, 1, 1}, {1, 8, 8, 1}, {1, 27, 216, 27, 1}, {1, 64, 1728, 1728, 64, 1}, {1, 125, 8000, 27000, 8000, 125, 1}, {1, 216, 27000, 216000, 216000, 27000, 216, 1}, {1, 343, 74088, 1157625, 2744000, 1157625, 74088, 343, 1}, {1, 512, 175616, 4741632, 21952000, 21952000, 4741632, 175616, 512, 1}, {1, 729, 373248, 16003008, 128024064, 250047000, 128024064, 16003008, 373248, 729, 1} MATHEMATICA c[n_, q_] = If[n == 0, 1, If[n == 1, 1, Product[(i - 1)^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, 10}] CROSSREFS Sequence in context: A172352 A141134 A176155 * A230153 A091648 A135707 Adjacent sequences:  A174124 A174125 A174126 * A174128 A174129 A174130 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Mar 09 2010 STATUS approved

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Last modified September 23 16:41 EDT 2020. Contains 337315 sequences. (Running on oeis4.)