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A217474 Sequence used for the formula for partial sums of odd powers of even-indexed Fibonacci numbers. 3
-1, 2, -14, 278, -15016, 2172632, -835765304, 851104689248, -2288258540319136, 16212819419809777952, -302332135138133434911104, 14824259801049378686209605248, -1909922987705772492088576593195136, 646210649409632730922299328304587407872 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This is the sequence c(m) used in the formula of Ozeki and Prodinger (see the references in A217472) for sum(F(2*k)^(2*m+1),k=1..n), m>=0, m>=0, given in A217472.

LINKS

Table of n, a(n) for n=0..13.

FORMULA

a(n) = pL(n)*C(n), with pL(n)=A217473(n) and C(n) = (1/5^n)*sum((-1)^(j-1)*binomial(2*n+1,j)*F(2*(n-j)+1)/L(2*(n-j)+1),j=0..n), n>=0, with F=A000045 and L=A000032.

EXAMPLE

a(2) = (1*4*11)*(-(1/25)*F(5)/L(5) + (1/5)*F(3)/(3) - (2/5)*F(1)/L(1)) = (1*4*11)*(-7/22) = -14.

CROSSREFS

Sequence in context: A156910 A279117 A018803 * A132695 A015015 A128087

Adjacent sequences:  A217471 A217472 A217473 * A217475 A217476 A217477

KEYWORD

sign,easy

AUTHOR

Wolfdieter Lang, Oct 12 2012

STATUS

approved

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Last modified August 4 21:20 EDT 2021. Contains 346455 sequences. (Running on oeis4.)