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A232602 Sum( k=0..n, k^p*q^k ), where p=3, q=-2. 10
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) = ((-1)^n*2^(n+1)*(27*n^3+27*n^2-9*n-3)+6)/81.

G.f.: 2*x*(1-8*x+4*x^2) / ( (x-1)*(2*x+1)^4 ). - R. J. Mathar, Nov 23 2014

EXAMPLE

a(3) = 0^3*2^0 - 1^3*2^1 + 2^3*2^2 - 3^3*2^3 = -186.

PROG

(PARI) a(n)=((-1)^n*2^(n+1)*(27*n^3+27*n^2-9*n-3)+6)/81;

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 August 17 23:58 EDT 2017. Contains 290682 sequences.