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 A232602 a(n) = Sum_{k=0..n} k^p*q^k, where p=3, q=-2. 12
 0, -2, 30, -186, 838, -3162, 10662, -33242, 97830, -275418, 748582, -1977306, 5100582, -12897242, 32060454, -78531546, 189903910, -454052826, 1074770982, -2521320410, 5867287590, -13554437082 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Stanislav Sykora, Table of n, a(n) for n = 0..1000 S. Sykora, Finite and Infinite Sums of the Power Series (k^p)(x^k), DOI 10.3247/SL1Math06.002, Section V. Index entries for linear recurrences with constant coefficients, signature (-7,-16,-8,16,16). FORMULA a(n) = 2*(1 - (-2)^n*(1 +3*n -9*n^2 -9*n^3))/27. G.f.: -2*x*(1-8*x+4*x^2) / ( (1-x)*(1+2*x)^4 ). - R. J. Mathar, Nov 23 2014 E.g.f.: (2/27)*(exp(x) - (1 +30*x -144*x^2 +72*x^3)*exp(-2*x)). - G. C. Greubel, Mar 31 2021 a(n) = - 7*a(n-1) - 16*a(n-2) - 8*a(n-3) + 16*a(n-4) + 16*a(n-5). - Wesley Ivan Hurt, Mar 31 2021 EXAMPLE a(3) = 0^3*2^0 - 1^3*2^1 + 2^3*2^2 - 3^3*2^3 = -186. MAPLE A232602:= n-> 2*(1 -(-2)^n*(1 +3*n -9*n^2 -9*n^3))/27; seq(A232602(n), n=0..35); # G. C. Greubel, Mar 31 2021 MATHEMATICA LinearRecurrence[{-7, -16, -8, 16, 16}, {0, -2, 30, -186, 838}, 40] (* G. C. Greubel, Mar 31 2021 *) PROG (PARI) a(n)=((-1)^n*2^(n+1)*(27*n^3+27*n^2-9*n-3)+6)/81; (Magma) [2*(1 -(-2)^n*(1 +3*n -9*n^2 -9*n^3))/27: n in [0..35]]; // G. C. Greubel, Mar 31 2021 (Sage) [2*(1 -(-2)^n*(1 +3*n -9*n^2 -9*n^3))/27 for n in (0..35)] # G. C. Greubel, Mar 31 2021 CROSSREFS Cf. A059841 (p=0,q=-1), A130472 (p=1,q=-1), A089594 (p=2,q=-1), A232599 (p=3,q=-1), A126646 (p=0,q=2), A036799 (p=1,q=2), A036800 (p=2,q=2), A036827 (p=3,q=2), A077925 (p=0,q=-2), A232600 (p=1,q=-2), A232601 (p=2,q=-2), A232603 (p=2,q=-1/2), A232604 (p=3,q=-1/2). Sequence in context: A078838 A267851 A089288 * A154413 A007030 A157054 Adjacent sequences: A232599 A232600 A232601 * A232603 A232604 A232605 KEYWORD sign,easy AUTHOR Stanislav Sykora, Nov 27 2013 STATUS approved

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Last modified September 23 11:05 EDT 2023. Contains 365544 sequences. (Running on oeis4.)