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%I #24 Mar 05 2021 10:15:35
%S 1,0,1,13,153,2089,33461,620166,13097377,310957991,8205571449,
%T 238367471761,7561422605881,260127000028908,9647591076297901,
%U 383769576967012081,16299953773597203585,736281113282903567521,35246262383544562907057,1782495208063575448970418
%N L(n,n), where L is defined as in A108299.
%C A108367(n) = L(n,-n).
%H Seiichi Manyama, <a href="/A108366/b108366.txt">Table of n, a(n) for n = 0..386</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Morgan-VoycePolynomials.html">Morgan-Voyce polynomials</a>
%F a(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} 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
%F a(n) ~ n^n * (1 - 2/n + 5/(2*n^2) - 31/(6*n^3) + 209/(24*n^4) - 173/(10*n^5) + ...). - _Vaclav Kotesovec_, Jan 06 2021
%t Join[{1,0,1}, Table[Sum[Binomial[n + k, 2*k] * (n-2)^k, {k,0,n}], {n,3,20}]] (* _Vaclav Kotesovec_, Jan 06 2021 *)
%o (PARI) a(n) = sum(k=0, n, binomial(n+k,2*k)*(n-2)^k); \\ _Jinyuan Wang_, Feb 25 2020
%Y Cf. A000312, A085478, A108299, A108367.
%K nonn
%O 0,4
%A _Reinhard Zumkeller_, Jun 01 2005
%E More terms from _Jinyuan Wang_, Feb 25 2020
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