The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A177971 Triangle of polynomial coefficients: p(x,n) = (1 - 2x)^(n + 1)*(1 + Sum_{k>=1} 2^(k - 1)*k^n*x^k). 0
 1, -1, 1, -3, 4, 1, -5, 14, -8, 1, -7, 32, -28, 16, 1, -9, 62, -36, 88, -32, 1, -11, 112, 104, 448, -176, 64, 1, -13, 198, 928, 2976, 240, 480, -128, 1, -15, 352, 4316, 20448, 17264, 5632, -960, 256, 1, -17, 638, 16500, 126968, 245872, 142752, 11200, 2432, -512, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Row sums are {0, 2, 2, 14, 74, 542, 4682, 47294, 545834, 7087262, 102247562, ...}. REFERENCES G. P. Egorychev, Integral Representation and the Computation of Combinatorial Sums, Translations of Mathematica Monographs, Volume 59, American Mathematical Society, Rhode Island, 1984, pages 9ff. LINKS FORMULA p(x,n) = (1 - 2x)^(n + 1)*(1 + Sum_{k>=1} 2^(k - 1)*k^n*x^k); t(n,m) = coefficients(t(n,m)). EXAMPLE {1, -1}, {1, -3, 4}, {1, -5, 14, -8}, {1, -7, 32, -28, 16}, {1, -9, 62, -36, 88, -32}, {1, -11, 112, 104, 448, -176, 64}, {1, -13, 198, 928, 2976, 240, 480, -128}, {1, -15, 352, 4316, 20448, 17264, 5632, -960, 256}, {1, -17, 638, 16500, 126968, 245872, 142752, 11200, 2432, -512}, {1, -19, 1184, 57472, 709232, 2490976, 2836928, 919552, 75776, -4864, 1024}, {1, -21, 2246, 190040, 3646816, 20950880, 41960896, 29090048, 6165760, 231168, 11776, -2048} MATHEMATICA p[x_, n_] = (1 - 2x)^(n + 1)*(1 + Sum[2^(k - 1)*k^n*x^k, {k, 1, Infinity}]); Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A133779 A137911 A019599 * A114156 A339964 A342915 Adjacent sequences:  A177968 A177969 A177970 * A177972 A177973 A177974 KEYWORD sign,tabf,less AUTHOR Roger L. Bagula, May 16 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 21 06:55 EDT 2021. Contains 345358 sequences. (Running on oeis4.)