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A108367 L(n,-n), where L is defined as in A108299. 2

%I #19 Feb 26 2020 00:30:35

%S 1,-2,5,-29,265,-3191,47321,-832040,16908641,-389806471,10049731549,

%T -286482047279,8946795882025,-303762892305614,11140078609864049,

%U -438857301101610929,18482410314337295233,-828657053219851847135,39406519321199703822581,-1981132660316876165976260

%N L(n,-n), where L is defined as in A108299.

%C A108366(n) = L(n,n).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Morgan-VoycePolynomials.html">Morgan-Voyce polynomials</a>

%F a(n) = (-1)^n * Product_{k=1..n} (n + 2*cos((2*k-1)*Pi/(2*n+1))) with Pi = 3.14...

%F a(n) = Sum_{k=0..n} (-1)^k*binomial(n+k,2*k)*(n+2)^k = b(n,-n-2), where b(n,x) are the Morgan-Voyce polynomials of A085478. - _Peter Bala_, May 01 2012

%o (PARI) a(n) = sum(k=0, n, (-1)^k*binomial(n+k,2*k)*(n+2)^k); \\ _Jinyuan Wang_, Feb 25 2020

%Y Cf. A000312, A085478, A108299, A108366.

%K sign

%O 0,2

%A _Reinhard Zumkeller_, Jun 01 2005

%E More terms from _Jinyuan Wang_, Feb 25 2020

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Last modified May 18 09:54 EDT 2024. Contains 372620 sequences. (Running on oeis4.)