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 A270307 Expansion of -(4*x^3+8*x^2+4*x+1)/(2*x^4+4*x^3+2*x^2-x-1). 1

%I

%S 1,3,7,7,21,27,57,95,169,303,529,943,1665,2943,5217,9215,16321,28863,

%T 51073,90367,159873,282879,500481,885503,1566721,2771967,4904449,

%U 8677375,15352833,27163647,48060417,85032959,150448129,266186751,470962177

%N Expansion of -(4*x^3+8*x^2+4*x+1)/(2*x^4+4*x^3+2*x^2-x-1).

%H Harvey P. Dale, <a href="/A270307/b270307.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-1, 2, 4, 2).

%F a(n) = (n+1)*Sum_{k=0..n}(Sum_{l=0..n-k}(binomial(k+1,l)*2^l*(-1)^(n-l-k)*binomial(n-2*l,n-l-k))/(k+1)).

%t LinearRecurrence[{-1,2,4,2},{1,3,7,7},50] (* _Harvey P. Dale_, Apr 11 2017 *)

%o (Maxima)

%o a(n):=(n+1)*sum(sum(binomial(k+1,l)*2^l*(-1)^(n-l-k)*binomial(n-2*l,n-l-k),l,0,n-k)/(k+1),k,0,n);

%Y Cf. A001405.

%K nonn

%O 0,2

%A _Vladimir Kruchinin_, Mar 15 2016

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Last modified September 17 16:57 EDT 2019. Contains 327136 sequences. (Running on oeis4.)