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If n is even, 2(n/2 + 1)! - 1; if n is odd, ((n + 1)/2 + 1)! - 1.
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%I #9 Mar 27 2020 09:47:29

%S 1,3,5,11,23,47,119,239,719,1439,5039,10079,40319,80639,362879,725759,

%T 3628799,7257599,39916799,79833599,479001599,958003199,6227020799,

%U 12454041599,87178291199,174356582399,1307674367999,2615348735999

%N If n is even, 2(n/2 + 1)! - 1; if n is odd, ((n + 1)/2 + 1)! - 1.

%t Table[If[EvenQ[n], 2(n/2 + 1)! - 1, ((n + 1)/2 + 1)! - 1], {n, 40}] (* _Alonso del Arte_, Feb 19 2020 *)

%o (PARI) a(n)=if(n%2, (n\2+2)!, (n/2+1)!*2) - 1 \\ _Charles R Greathouse IV_, Mar 27 2020

%Y s(n) = s(n + 1), where s = A030298.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_

%E Better description and more terms from _Erich Friedman_.