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%I #16 Apr 07 2021 15:39:08
%S 1,3,9,32,147,844,5765,45366,403207,3991688,43545609,518918410,
%T 6706022411,93405312012,1394852659213,22230464256014,376610217984015,
%U 6758061133824016,128047474114560017,2554547108585472018,53523844179886080019,1175091669949317120020
%N a(n) = n! + (n-1)! + n-2.
%H Michael De Vlieger, <a href="/A341302/b341302.txt">Table of n, a(n) for n = 1..449</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.
%F E.g.f.: (1/(1 - x) - exp(x)) * (2 - x) - log(1 - x). - _Ilya Gutkovskiy_, Feb 15 2021
%t Array[#2 + (#1 + 1) #2 + #1 - 1 & @@ {#, #!} &, 22, 0] (* _Michael De Vlieger_, Apr 07 2021 *)
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Feb 13 2021
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