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 A144457 Coefficients of polynomials based on the generalized factorial at k=2 (A001147): b(n)=b(n-1+k; a(n)=b(n)*a(n-1); p(x,n)=If[n == 0, 1, a(n - 1)*(x - a(n - 1))*Product[x + 1/b(i), {i, 1, n - 1}]]. 0
 1, -1, 1, -3, -8, 3, -15, -119, -217, 15, -105, -1574, -7440, -10954, 105, -945, -22679, -194646, -702874, -892281, 945, -10395, -363824, -4885615, -31288480, -94892945, -108046896, 10395, -135135, -6486479, -124999827, -1232430275, -6521470845, -17442096461, -18261339153, 135135 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Row sums are: {1, 0, -8, -336, -19968, -1812480, -239477760, -43588823040, -10461389783040, -3201186759966720, -1216451002230374400}. LINKS FORMULA b(n)=b(n-1+k; a(n)=b(n)*a(n-1); p(x,n)=If[n == 0, 1, a(n - 1)*(x - a(n - 1))*Product[x + 1/b(i), {i, 1, n - 1}]]; t(n,m)=coefficients(p(x,n)). EXAMPLE {1}, {-1, 1}, {-3, -8, 3}, {-15, -119, -217, 15}, {-105, -1574, -7440, -10954,105}, {-945, -22679, -194646, -702874, -892281,945}, {-10395, -363824, -4885615, -31288480, -94892945, -108046896, 10395}, {-135135, -6486479, -124999827, -1232430275, -6521470845, -17442096461, -18261339153, 135135} MATHEMATICA Clear[a, b, p, x, n]; k = 2; b[0] = 1; b[n_] := b[n] = b[n - 1] + k; a[0] = 1; a[n_] := a[n] = b[n]*a[n - 1]; p[x_, n_] = If[n == 0, 1, a[n - 1]*(x - a[n - 1])*Product[x + 1/b[i], {i, 1, n - 1}]]; Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[%] CROSSREFS Cf. A001147. Sequence in context: A046543 A233129 A035292 * A220138 A146975 A046970 Adjacent sequences:  A144454 A144455 A144456 * A144458 A144459 A144460 KEYWORD sign,uned AUTHOR Roger L. Bagula and Gary W. Adamson, Oct 07 2008 STATUS approved

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Last modified August 6 00:36 EDT 2021. Contains 346493 sequences. (Running on oeis4.)