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A232603 2^n*sum( k=0..n, k^p*q^k ), where p=2, q=-1/2. 8
0, -1, 2, -5, 6, -13, 10, -29, 6, -69, -38, -197, -250, -669, -1142, -2509, -4762, -9813, -19302, -38965, -77530, -155501, -310518, -621565, -1242554, -2485733, -4970790, -9942309, -19883834, -39768509, -79536118 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The factor 2^n (i.e. |1/q|^n) is present to keep the values integer.

See also A232600 and references therein for integer values of q.

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 (-1,3,5,2).

FORMULA

a(n) = ((-1)^n*(9*n^2+12*n+2)-2^(n+1))/27.

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

EXAMPLE

a(3) = 2^3 * [0^2/2^0 - 1^2/2^1 + 2^2/2^2 - 3^2/2^3] = -5.

PROG

(PARI) a(n)=((-1)^n*(9*n^2+12*n+2)-2^(n+1))/27;

CROSSREFS

Cf. A001045 (p=0,q=-1/2), A053088 (p=1,q=-1/2), A232604 (p=3,q=-1/2), A000225 (p=0,q=1/2), A000295 and A125128 (p=1,q=1/2), A047520 (p=2,q=1/2), A213575 (p=3,q=1/2), A232599 (p=3,q=-1), A232600 (p=1,q=-2), A232601 (p=2,q=-2), A232602 (p=3,q=-2).

Sequence in context: A057683 A277012 A277022 * A069480 A100613 A070911

Adjacent sequences:  A232600 A232601 A232602 * A232604 A232605 A232606

KEYWORD

sign,easy

AUTHOR

Stanislav Sykora, Nov 27 2013

STATUS

approved

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Last modified August 22 01:16 EDT 2017. Contains 290942 sequences.