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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

%I

%S 1,2,2,3,4,3,16,24,24,16,45,144,162,144,45,192,480,1152,1152,480,192,

%T 1050,2400,4500,9600,4500,2400,1050,6912,15120,25920,43200,43200,

%U 25920,15120,6912,52920,112896,185220,282240,220500,282240,185220,112896

%N 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))

%C Row sums are:

%C {1, 4, 10, 80, 540, 3648, 25500, 182304, 1487052,...}

%D Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), pp. 165-66

%F c(n)=Gamma[n-2]/Gamma[m];

%F m=2;f(n)=c(n)/(n*c(n-1);

%F t(n,k)=c(n)*n*f(n)/(f(n-k)*f(k))

%e {1},

%e {2, 2},

%e {3, 4, 3},

%e {16, 24, 24, 16},

%e {45, 144, 162, 144, 45},

%e {192, 480, 1152, 1152, 480, 192},

%e {1050, 2400, 4500, 9600, 4500, 2400, 1050},

%e {6912, 15120, 25920, 43200, 43200, 25920, 15120, 6912},

%e {52920, 112896, 185220, 282240, 220500, 282240, 185220, 112896, 52920}

%t Clear[c, n, x, p]

%t m = 2;

%t c[n_] := If[n <= 2, 1, Gamma[n - 2]/Gamma[m]]

%t f[n_] = (c[n]/(n*c[n - 1]))

%t t[n_, k_] = c[n]*n*f[n]/(f[n - k]*f[k])

%t Table[Table[t[n, k], {k, 1, n - 1}], {n, 2, 10}]

%t Flatten[%]

%K nonn,tabl,uned

%O 2,2

%A _Roger L. Bagula_, Dec 19 2009

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Last modified September 16 02:16 EDT 2019. Contains 327088 sequences. (Running on oeis4.)