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A178126 A triangle of polynomial coefficients:p(x,n)=If[n == 0, 1, n!*(Binomial[x + n, n] - Binomial[x, n])] 0
1, 1, 2, 4, 6, 9, 9, 24, 56, 24, 16, 120, 250, 275, 50, 25, 720, 1884, 1350, 960, 90, 36, 5040, 12348, 14896, 5145, 2695, 147, 49, 40320, 114624, 105056, 80416, 15680, 6496, 224, 64, 362880, 986256, 1282284, 605556, 336609, 40824, 13986, 324, 81, 3628800 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Row sums are:(nearly (n-1)!)

{1, 1, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800,...}.

A special case of Hilbert polynomials when the degree is equal to n.

REFERENCES

Brendan Hassett, Introduction to algebraic Geometry,Cambridge University Press. New York,2007, page 214

LINKS

Table of n, a(n) for n=0..46.

FORMULA

p(x,n)=If[n == 0, 1, n!*(Binomial[x + n, n] - Binomial[x, n])];

t(n,m)=coefficients(p(x,n))

EXAMPLE

{1},

{1},

{2, 4},

{6, 9, 9},

{24, 56, 24, 16},

{120, 250, 275, 50, 25},

{720, 1884, 1350, 960, 90, 36},

{5040, 12348, 14896, 5145, 2695, 147, 49},

{40320, 114624, 105056, 80416, 15680, 6496, 224, 64},

{362880, 986256, 1282284, 605556, 336609, 40824, 13986, 324, 81},

{3628800, 10991520, 11727000, 9582200, 2693250, 1171380, 94500, 27600, 450, 100}

MATHEMATICA

p[x_, n_] := If[n == 0, 1, n!*(Binomial[x + n, n] - Binomial[x, n])];

Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}];

Flatten[%]

CROSSREFS

Cf. A139167

Sequence in context: A084407 A114526 A333387 * A162202 A210380 A228359

Adjacent sequences:  A178123 A178124 A178125 * A178127 A178128 A178129

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, May 20 2010

STATUS

approved

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Last modified August 6 09:38 EDT 2020. Contains 336245 sequences. (Running on oeis4.)