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 A176667 A triangle of polynomial coefficients:p(x,n)=Sum[(k + 1)^n*Binomial[x, k], {k, 0, Infinity}]/2^(x - n) 0
 1, 2, 1, 4, 5, 1, 8, 18, 9, 1, 16, 54, 51, 14, 1, 32, 140, 220, 115, 20, 1, 64, 328, 750, 685, 225, 27, 1, 128, 784, 2044, 3080, 1785, 399, 35, 1, 256, 2096, 5068, 10220, 10465, 4088, 658, 44, 1, 512, 4704, 16776, 25284, 43806, 30681, 8484, 1026, 54, 1, 1024 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums are:A007582; {1, 3, 10, 36, 136, 528, 2080, 8256, 32896, 131328, 524800,...}. LINKS FORMULA p(x,n)=Sum[(k + 1)^n*Binomial[x, k], {k, 0, Infinity}]/2^(x - n); t(n,m)=coefficients(p(x,n)) EXAMPLE {1}, {2, 1}, {4, 5, 1}, {8, 18, 9, 1}, {16, 54, 51, 14, 1}, {32, 140, 220, 115, 20, 1}, {64, 328, 750, 685, 225, 27, 1}, {128, 784, 2044, 3080, 1785, 399, 35, 1}, {256, 2096, 5068, 10220, 10465, 4088, 658, 44, 1}, {512, 4704, 16776, 25284, 43806, 30681, 8484, 1026, 54, 1}, {1024, 2496, 61920, 79980, 118020, 163569, 79905, 16290, 1530, 65, 1} MATHEMATICA Clear[p, x, n] p[x_, n_] = Sum[(k + 1)^n*Binomial[x, k], {k, 0, Infinity}]/2^(x - n); Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]; Flatten[%] CROSSREFS Cf. A007582 Sequence in context: A124237 A123876 A114164 * A126182 A154342 A143494 Adjacent sequences:  A176664 A176665 A176666 * A176668 A176669 A176670 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Apr 23 2010 STATUS approved

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Last modified May 18 19:58 EDT 2021. Contains 344002 sequences. (Running on oeis4.)