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 A143185 A designed symmetrical triangle sequence: t(n,m)=If[m*(n - m) == 0, 1, (1 + Abs[(1 + n - m) - (1 + m)])*Binomial[n, m]]. 0
 1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 12, 6, 12, 1, 1, 20, 20, 20, 20, 1, 1, 30, 45, 20, 45, 30, 1, 1, 42, 84, 70, 70, 84, 42, 1, 1, 56, 140, 168, 70, 168, 140, 56, 1, 1, 72, 216, 336, 252, 252, 336, 216, 72, 1, 1, 90, 315, 600, 630, 252, 630, 600, 315, 90, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Row sums are: {1, 3, 13, 31, 81, 171, 393, 799, 1753, 3523}. LINKS FORMULA t(n,m)=If[m*(n - m) == 0, 1, (1 + Abs[(1 + n - m) - (1 + m)])*Binomial[n, m]]. EXAMPLE {1}, {1, 1}, {1, 2, 1}, {1, 6, 6, 1}, {1, 12, 6, 12, 1}, {1, 20, 20, 20, 20, 1}, {1, 30, 45, 20, 45, 30, 1}, {1, 42, 84, 70, 70, 84, 42, 1}, {1, 56, 140, 168, 70, 168, 140, 56, 1}, {1, 72, 216, 336, 252, 252, 336, 216, 72, 1}, {1, 90, 315, 600, 630, 252, 630, 600, 315, 90, 1} MATHEMATICA Clear[t, n, m]; t[n_, m_] = If[m*(n - m) == 0, 1, (1 + Abs[(1 + n - m) - (1 + m)])*Binomial[n, m]]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A283795 A168641 A255914 * A157635 A075798 A155864 Adjacent sequences:  A143182 A143183 A143184 * A143186 A143187 A143188 KEYWORD nonn,uned AUTHOR Roger L. Bagula and Gary W. Adamson, Oct 17 2008 STATUS approved

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Last modified September 24 07:28 EDT 2020. Contains 337317 sequences. (Running on oeis4.)