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 A174860 A triangle sequence of polynomial coefficients:p(x,n)=Sum[Eulerian[n+1, k]*(-x)^k*Sum[StirlingS2[n, m]*x^m, {m, 0, n - k}], {k, 0, n}] 0
 1, 0, 1, 0, 1, -3, 0, 1, -8, -21, 0, 1, -19, -110, 281, 0, 1, -42, -528, 2813, 2508, 0, 1, -89, -2439, 23770, 25700, -105023, 0, 1, -184, -10967, 180843, 237505, -2253624, -439709, 0, 1, -375, -48180, 1283751, 2208948, -41164774, 4807292, 93525833, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Row sums are: {1, 1, -2, -28, 153, 4752, -58080, -2286135, 60612496, 2179207812, -125325232468,...}. LINKS FORMULA p(x,n)=Sum[Eulerian[n+1, k]*(-x)^k*Sum[StirlingS2[n, m]*x^m, {m, 0, n - k}], {k, 0, n}]; t(n,m)=coefficients(p(x,n)) EXAMPLE {1}, {0, 1}, {0, 1, -3}, {0, 1, -8, -21}, {0, 1, -19, -110, 281}, {0, 1, -42, -528, 2813, 2508}, {0, 1, -89, -2439, 23770, 25700, -105023}, {0, 1, -184, -10967, 180843, 237505, -2253624, -439709}, {0, 1, -375, -48180, 1283751, 2208948, -41164774, 4807292, 93525833}, {0, 1, -758, -207450, 8687453, 22088335, -679447801, 423149836, 3295732928, -890794732}, {0, 1, -1525, -878429, 56832244, 238463701, -10478964222, 14125711299, 100154063565, -81834448272, -147586010830} MATHEMATICA Clear[p, x, n]; << DiscreteMath`Combinatorica` p[x_, n_] = Sum[Eulerian[n+1, k]*(-x)^k*Sum[StirlingS2[n, m]*x^m, {m, 0, n - k}], {k, 0, n}]; Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A161129 A011074 A020816 * A157391 A099097 A152150 Adjacent sequences:  A174857 A174858 A174859 * A174861 A174862 A174863 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Mar 31 2010 STATUS approved

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Last modified March 24 19:48 EDT 2019. Contains 321448 sequences. (Running on oeis4.)