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 A174833 A triangular sequence of polynomial coefficients:p(x,n)=Sum[Eulerian[n + 1, k]*Product[x + i, {i, 0, n - k + 1}]*(-x)^k, {k, 0, n}]/x 0
 1, 2, 2, 6, 3, -5, -2, 24, -16, -64, -24, 120, -350, -679, -151, 74, 16, 720, -5076, -6746, 1198, 2692, 544, 5040, -73332, -55628, 80239, 68081, 8858, -2000, -272, 40320, -1135296, -18712, 2522252, 1417588, -83312, -155392, -19840, 362880 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums are: {1, 4, 2, -80, -970, -6668, 30986, 2567608, 67974542, 1084990396, -6362961886,...} LINKS FORMULA p(x,n)=Sum[Eulerian[n + 1, k]*Product[x + i, {i, 0, n - k + 1}]*(-x)^k, {k, 0, n}]/x t(n,m)=coefficients(p(x,n)) EXAMPLE {1}, {2, 2}, {6, 3, -5, -2}, {24, -16, -64, -24}, {120, -350, -679, -151, 74, 16}, {720, -5076, -6746, 1198, 2692, 544}, {5040, -73332, -55628, 80239, 68081, 8858, -2000, -272}, {40320, -1135296, -18712, 2522252, 1417588, -83312, -155392, -19840}, {362880, -19214064, 19785852, 68794296, 21423037, -14938145, -7669234, -662752, 84736, 7936}, {3628800, -356968800, 901740888, 1768795280, -83612926, -876416978, -291269756, 6024320, 12008192, 1061376}, {39916800, -7267692960, 33899921496, 41987822092, -30465270802, -40831787105, -7672559733, 2867304822, 1021675584, 63226000, -5164288, -353792} MATHEMATICA << DiscreteMath`Combinatorica` Clear[p, n, x, k]; p[x, 0] := 1; p[x_, n_] := Sum[Eulerian[n + 1, k]* Product[x + i, {i, 0, n - k + 1}]*(-x)^k, {k, 0, n}]/x; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]; Flatten[%] CROSSREFS Cf. A174789 Sequence in context: A277011 A277021 A275037 * A085738 A227608 A276484 Adjacent sequences:  A174830 A174831 A174832 * A174834 A174835 A174836 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Mar 30 2010 STATUS approved

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Last modified August 22 02:44 EDT 2019. Contains 326169 sequences. (Running on oeis4.)