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 A171830 Triangular sequence based on an hypergeometric form: c(n)=Gamma[n-2]/Gamma[m]; m=2;f(n)=c(n)/(n*c(n-1); t(n,k)=c(n)*n*f(n)/(f(n-k)*f(k)) 0
 1, 2, 2, 3, 4, 3, 16, 24, 24, 16, 45, 144, 162, 144, 45, 192, 480, 1152, 1152, 480, 192, 1050, 2400, 4500, 9600, 4500, 2400, 1050, 6912, 15120, 25920, 43200, 43200, 25920, 15120, 6912, 52920, 112896, 185220, 282240, 220500, 282240, 185220, 112896 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS Row sums are: {1, 4, 10, 80, 540, 3648, 25500, 182304, 1487052,...} REFERENCES Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), pp. 165-66 LINKS FORMULA c(n)=Gamma[n-2]/Gamma[m]; m=2;f(n)=c(n)/(n*c(n-1); t(n,k)=c(n)*n*f(n)/(f(n-k)*f(k)) EXAMPLE {1}, {2, 2}, {3, 4, 3}, {16, 24, 24, 16}, {45, 144, 162, 144, 45}, {192, 480, 1152, 1152, 480, 192}, {1050, 2400, 4500, 9600, 4500, 2400, 1050}, {6912, 15120, 25920, 43200, 43200, 25920, 15120, 6912}, {52920, 112896, 185220, 282240, 220500, 282240, 185220, 112896, 52920} MATHEMATICA Clear[c, n, x, p] m = 2; c[n_] := If[n <= 2, 1, Gamma[n - 2]/Gamma[m]] f[n_] = (c[n]/(n*c[n - 1])) t[n_, k_] = c[n]*n*f[n]/(f[n - k]*f[k]) Table[Table[t[n, k], {k, 1, n - 1}], {n, 2, 10}] Flatten[%] CROSSREFS Sequence in context: A164975 A253889 A228754 * A071506 A125920 A176360 Adjacent sequences:  A171827 A171828 A171829 * A171831 A171832 A171833 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Dec 19 2009 STATUS approved

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Last modified August 25 05:19 EDT 2019. Contains 326318 sequences. (Running on oeis4.)