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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

Table of n, a(n) for n=2..45.

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.)