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 A174859 A triangle sequence of polynomial coefficients:p(x,n)=Sum[Binomial[n, k]*(-x)^k*Sum[StirlingS2[n, m]*x^m, {m, 0, n - k}], {k, 0, n}] 0
 1, 0, 1, 0, 1, -1, 0, 1, 0, -5, 0, 1, 3, -16, 15, 0, 1, 10, -40, 25, 56, 0, 1, 25, -81, -30, 370, -455, 0, 1, 56, -119, -469, 1841, -1960, -237, 0, 1, 119, -22, -2527, 7448, -5768, -7420, 16947, 0, 1, 246, 766, -10359, 24627, -2289, -76692, 126504, -64220, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,10 COMMENTS Row sums are: {1, 1, 0, -4, 3, 52, -170, -887, 8778, -1416, -415734,...}. REFERENCES J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 77. LINKS FORMULA p(x,n)=Sum[Binomial[n, 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, -1}, {0, 1, 0, -5}, {0, 1, 3, -16, 15}, {0, 1, 10, -40, 25, 56}, {0, 1, 25, -81, -30, 370, -455}, {0, 1, 56, -119, -469, 1841, -1960, -237}, {0, 1, 119, -22, -2527, 7448, -5768, -7420, 16947}, {0, 1, 246, 766, -10359, 24627, -2289, -76692, 126504, -64220}, {0, 1, 501, 4265, -36320, 60215, 119760, -570627, 784245, -248280, -529494} MATHEMATICA Clear[p, x, n]; p[x_, n_] = Sum[Binomial[n, 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 Cf. A008299 Sequence in context: A117015 A325736 A334364 * A274619 A230844 A054672 Adjacent sequences:  A174856 A174857 A174858 * A174860 A174861 A174862 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Mar 31 2010 STATUS approved

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Last modified January 26 05:13 EST 2022. Contains 350572 sequences. (Running on oeis4.)