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%I #24 Oct 23 2023 12:31:14
%S 18,208,1372,7632,39050,190112,895524,4120528,18629652,83088096,
%T 366560568,1602837280,6956911962,30007067456,128736063316,
%U 549740689872,2338025684540,9907917740128,41853370268424,176294674155104,740683257681988,3104678088923328,12986226585328232
%N a(n) = (2*n-3)*4^(n-1) - 2*binomial(2*n, n-1).
%H Sihuang Hu and Gabriele Nebe, <a href="https://arxiv.org/abs/1805.01196">Strongly perfect lattices sandwiched between Barnes-Wall lattices</a>, arXiv:1805.01196 [math.NT], 2018. See p. 21.
%F E.g.f.: (3 + 12*x + 8*x^2 - 3*exp(4*x) + 8*exp(4*x)*x - 8*exp(2*x)*I_1(2*x) )/4, where I_1(.) is the modified Bessel function of the first kind. - _Bruno Berselli_, May 08 2018
%F (n+1)*(2*n^2-7*n+7)*a(n) - 2*n*(4*n-5)*(2*n-3)*a(n-1) + 8*(2*n-3)*(2*n^2-3*n+2)*a(n-2) = 0. - _R. J. Mathar_, May 08 2018
%t Table[(2 n - 3) 4^(n - 1) - 2 Binomial[2 n, n - 1], {n, 3, 40}]
%o (Magma) [(2*n-3)*4^(n-1)-2*Binomial(2*n, n-1): n in [3..20]];
%o (PARI) a(n) = (2*n-3)*4^(n-1) - 2*binomial(2*n, n-1) \\ _Charles R Greathouse IV_, Oct 23 2023
%Y Cf. A144704, A162551.
%K nonn,easy
%O 3,1
%A _Vincenzo Librandi_, May 08 2018
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