This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A293656 #37 Nov 07 2023 03:16:54
%S A293656 1,3,12,30,120,315,1344,3780,17280,51975,253440,810810,4193280,
%T A293656 14189175,77414400,275675400,1579253760,5892561675,35300966400,
%U A293656 137493105750,858370867200,3478575575475,22562891366400,94870242967500,637646929920000,2774954606799375
%N A293656 a(n) = binomial(n+1,2)*n!/n!!.
%C A293656 It appears that the difference between a(n)/a(n-1) and a(n-1)/a(n-2) approaches some factor, 5 < x < 7, as n --> oo.
%C A293656 It appears that 3|a(n) for n > 1.
%D A293656 L. Euler and J. L. Lagrange, Elements of Algebra, J. Johnson and Co. 1810. See pages 332-335.
%F A293656 a(n) = ((n*(n+1))/2)/(Product_{i=0..floor((n-1)/2),n-2*i}/Product_{i=1..n}).
%F A293656 From _Chai Wah Wu_, Feb 07 2018: (Start)
%F A293656 a(n) = n*(n+1)!!/2.
%F A293656 a(n)/a(n-1) = ((n+1)!!/n!!)*(n/(n-1)) = n/b*(n-1) if n is even and n*Pi/(2*b*(n-1)) if n is odd where b = Integral_{x=0..(Pi/2)} sin^(n+1)*x dx.
%F A293656 Since b -> 0 as n -> oo, a(n)/a(n-1) is unbounded as n -> oo. On the other hand, a(n)/a(n-1) and a(n-1)/a(n-2) differ by a multiplicative factor of approximately Pi/2.
%F A293656 (End)
%e A293656 For n = 6, a(6) = binomial(6+1,2)/(6!!/6!) = 315.
%t A293656 Table[Binomial[n+1,2] n!/n!!,{n,30}] (* _Harvey P. Dale_, Jul 27 2021 *)
%Y A293656 Cf. A000217, A000142, A006882.
%K A293656 nonn
%O A293656 1,2
%A A293656 _Justin Gaetano_, Feb 06 2018