A304202 a(n) = (2*n-3)*4^(n-1) - 2*binomial(2*n, n-1).
18, 208, 1372, 7632, 39050, 190112, 895524, 4120528, 18629652, 83088096, 366560568, 1602837280, 6956911962, 30007067456, 128736063316, 549740689872, 2338025684540, 9907917740128, 41853370268424, 176294674155104, 740683257681988, 3104678088923328, 12986226585328232
Offset: 3
Links
- Sihuang Hu and Gabriele Nebe, Strongly perfect lattices sandwiched between Barnes-Wall lattices, arXiv:1805.01196 [math.NT], 2018. See p. 21.
Programs
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Magma
[(2*n-3)*4^(n-1)-2*Binomial(2*n, n-1): n in [3..20]];
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Mathematica
Table[(2 n - 3) 4^(n - 1) - 2 Binomial[2 n, n - 1], {n, 3, 40}] -
PARI
a(n) = (2*n-3)*4^(n-1) - 2*binomial(2*n, n-1) \\ Charles R Greathouse IV, Oct 23 2023
Formula
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
(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