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A217474 Sequence used for the formula for partial sums of odd powers of even-indexed Fibonacci numbers. 3

%I

%S -1,2,-14,278,-15016,2172632,-835765304,851104689248,

%T -2288258540319136,16212819419809777952,-302332135138133434911104,

%U 14824259801049378686209605248,-1909922987705772492088576593195136,646210649409632730922299328304587407872

%N Sequence used for the formula for partial sums of odd powers of even-indexed Fibonacci numbers.

%C 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.

%F 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.

%e 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.

%K sign,easy

%O 0,2

%A _Wolfdieter Lang_, Oct 12 2012

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Last modified September 16 16:40 EDT 2021. Contains 347473 sequences. (Running on oeis4.)