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 A229702 Expansion of 1/((1-x)^4*(1-6x)). 0
 1, 10, 70, 440, 2675, 16106, 96720, 580440, 3482805, 20897050, 125382586, 752295880, 4513775735, 27082654970, 162495930500, 974975583816, 5849853503865, 35099121024330, 210594726147310, 1263568356885400, 7581410141314171 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This sequence was chosen to illustrate a way to match generating functions and closed-form solutions. The general term associated with the generating function 1/((1-s*x)^4*(1-r*x)) with r>s>=1 is a(n) = [ r^(n+4) - s^(n+1)*(s^3 + s^2*(r-s)*binomial(n+4,1) + s*(r-s)^2*binomial(n+4,2)+(r-s)^3*binomial(n+4,3))]/(r-s)^4. LINKS Index entries for linear recurrences with constant coefficients, signature (10,-30,40,-25,6). FORMULA a(n) = (6^(n+4) - (1 + 5*C(n+4,1) + 25*C(n+4,2) + 125*C(n+4,3)))/625 = (6^(n+5) - (125*n^3 + 1200*n^2 + 3805*n + 4026))/3750. EXAMPLE a(3) = (6^8 - (125*3^3  + 1200*3^2 + 3805*3 + 4026))/3750 = 440. CROSSREFS Cf. A002663, A097786, A097788, A097790. Sequence in context: A122892 A125347 A005465 * A337992 A257114 A037600 Adjacent sequences:  A229699 A229700 A229701 * A229703 A229704 A229705 KEYWORD nonn,easy AUTHOR Yahia Kahloune, Sep 27 2013 STATUS approved

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Last modified May 8 09:57 EDT 2021. Contains 343666 sequences. (Running on oeis4.)