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 A166341 Coefficients of recursive differential polynomial:p(x,3)=x*(x^2 + 10*x + 1)/(1 - x)^4;p(x, n) = x*D[p[x, n - 1], x] 0
 1, 1, 1, 1, 10, 1, 1, 23, 23, 1, 1, 50, 138, 50, 1, 1, 105, 614, 614, 105, 1, 1, 216, 2367, 4912, 2367, 216, 1, 1, 439, 8397, 31483, 31483, 8397, 439, 1, 1, 886, 28264, 176314, 314830, 176314, 28264, 886, 1, 1, 1781, 91880, 903104, 2632034, 2632034, 903104 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Row sums are:{1, 2, 12, 48, 240, 1440, 10080, 80640, 725760, 7257600, 79833600,...} REFERENCES Douglas C. Montgomery and Lynwood A. Johnson, Forecasting and Time Series Analysis, MaGraw-Hill, New York, 1976, page 91 LINKS FORMULA p(x,0)= 1/(1 - x); p(x,1)= x/(1 - x)^2; p(x,2)= x*(1 + x)/(1 - x)^3; p(x,3)= x*(x^2 + 10*x + 1)/(1 - x)^4; p(x,n)= x*D[p[x, n - 1], x] EXAMPLE {1}, {1, 1}, {1, 10, 1}, {1, 23, 23, 1}, {1, 50, 138, 50, 1}, {1, 105, 614, 614, 105, 1}, {1, 216, 2367, 4912, 2367, 216, 1}, {1, 439, 8397, 31483, 31483, 8397, 439, 1}, {1, 886, 28264, 176314, 314830, 176314, 28264, 886, 1}, {1, 1781, 91880, 903104, 2632034, 2632034, 903104, 91880, 1781, 1}, {1, 3572, 291669, 4347456, 19481898, 31584408, 19481898, 4347456, 291669, 3572, 1} MATHEMATICA p[x_, 0] := 1/(1 - x); p[x_, 1] := x/(1 - x)^2; p[x_, 2] := x*(1 + x)/(1 - x)^3; p[x_, 3] := x*(x^2 + 10*x + 1)/(1 - x)^4; p[x_, n_] := p[x, n] = x*D[p[x, n - 1], x] a = Table[CoefficientList[FullSimplify[ExpandAll[(1 - x)^(n + 1)*p[x, n]/x]], x], {n, 1, 11}]; Flatten[a] Table[Apply[Plus, CoefficientList[FullSimplify[ExpandAll[(1 - x)^(n + 1)*p[x, n]/x]], x]], {n, 1, 11}]; CROSSREFS Sequence in context: A143683 A146773 A202941 * A113280 A159041 A154979 Adjacent sequences:  A166338 A166339 A166340 * A166342 A166343 A166344 KEYWORD nonn,uned AUTHOR Roger L. Bagula, Oct 12 2009 STATUS approved

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Last modified January 18 00:43 EST 2022. Contains 350410 sequences. (Running on oeis4.)