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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 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.)