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A232601 Sum[k=0..n] k^p*q^k for p=2,q=-2. 10
0, -2, 14, -58, 198, -602, 1702, -4570, 11814, -29658, 72742, -175066, 414758, -969690, 2241574, -5131226, 11645990, -26233818, 58700838, -130567130, 288863270, -635980762, 1394062374, -3043511258, 6620165158 (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 (-5,-6,4,8).

FORMULA

a(n) = ((-1)^n*2^(n+1)*(9*n^2+6*n-1)+2)/27.

G.f.: -2*x*(-1+2*x) / ( (x-1)*(2*x+1)^3 ). - R. J. Mathar, Nov 23 2014

EXAMPLE

a(3) = 0^2*2^0 - 1^2*2^1 + 2^2*2^2 - 3^2*2^3 = -58.

MATHEMATICA

LinearRecurrence[{-5, -6, 4, 8}, {0, -2, 14, -58}, 30] (* Harvey P. Dale, Aug 20 2015 *)

PROG

(PARI) S2M2(n)=((-1)^n*2^(n+1)*(9*n^2+6*n-1)+2)/27;

v = vector(10001); for(k=1, #v, v[k]=S2M2(k-1))

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), A232602 (p=3,q=-2), A232603 (p=2,q=-1/2), A232604 (p=3,q=-1/2).

Sequence in context: A115027 A114146 A096367 * A285153 A232370 A174704

Adjacent sequences:  A232598 A232599 A232600 * A232602 A232603 A232604

KEYWORD

sign,easy,changed

AUTHOR

Stanislav Sykora, Nov 27 2013

STATUS

approved

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Last modified June 25 06:13 EDT 2017. Contains 288709 sequences.