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%I #14 Sep 30 2024 12:53:21
%S 2,2,8,228,3086,32998,336238,3533094,39574232,477773836,6222604044,
%T 87162325914,1307616361780,20922578067962,355686650879752,
%U 6402370841201732,121645089807866376,2432901968797147330,51090942024922302314,1124000727228733234894
%N a(n) = n!-6*Catalan(n)+5*2^n+4*binomial(n,2)-2*Fibonacci(n)-14*n+20.
%H Paolo Xausa, <a href="/A341303/b341303.txt">Table of n, a(n) for n = 3..400</a>
%H Michael Engen and Vincent Vatter, <a href="https://doi.org/10.1080/00029890.2021.1835384">Containing all permutations</a>, Amer. Math. Monthly, 128 (2021), 4-24; <a href="https://arxiv.org/abs/1810.08252">arXiv preprint</a>, arXiv:1810.08252 [math.CO], 2018-2020.
%t Table[n! - 6*CatalanNumber[n] - 2*Fibonacci[n] + 5*(4 + 2^n) + 2*n*(n - 8), {n, 3, 25}] (* _Paolo Xausa_, Sep 30 2024 *)
%Y Cf. A000045, A000108.
%K nonn
%O 3,1
%A _N. J. A. Sloane_, Feb 13 2021