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 A067624 #41 Jul 02 2025 16:02:01
%S A067624 1,8,384,46080,10321920,3715891200,1961990553600,1428329123020800,
%T A067624 1371195958099968000,1678343852714360832000,2551082656125828464640000,
%U A067624 4714400748520531002654720000,10409396852733332453861621760000
%N A067624 a(n) = 2^(2*n)*(2*n)!.
%C A067624 For n >= 1, a(n) equals the absolute value of the determinant of the 4n X 4n matrix with i's along the superdiagonal (where i is the imaginary unit), and 2, 3, 4, ... 4*n along the subdiagonal, and 0's everywhere else. (See Mathematica code below.) - _John M. Campbell_, Jun 04 2011
%H A067624 Vincenzo Librandi, <a href="/A067624/b067624.txt">Table of n, a(n) for n = 0..200</a>
%F A067624 a(n) = A000165(2*n) where A000165(k) are the double factorial numbers 2^k*k!=(2k)!!. - Corrected by _Johannes W. Meijer_, Jul 05 2009
%F A067624 a(n) = (4*n)!! = 2^(2*n)*(2*n)!. - _Johannes W. Meijer_, Jul 06 2009
%F A067624 sqrt((1+cos(x))/2) = Sum_{n>=0} (-1)^n * x^(2*n) / a(n).
%F A067624 a(n) = (A280442(n)/A046161(n))/(A223067(n)/A223068(n)). - _Johannes W. Meijer_, Jan 05 2017
%F A067624 From _Amiram Eldar_, Jul 12 2020: (Start)
%F A067624 Sum_{n>=0} 1/a(n) = cosh(1/2).
%F A067624 Sum_{n>=0} (-1)^n/a(n) = cos(1/2). (End)
%p A067624 for n from 0 to 30 by 2 do printf(`%d,`,2^(n)*(n)!) od: # _James Sellers_, Feb 11 2002
%p A067624 A067624 := n -> 2^(2*n)*(2*n)!: seq(A067624(n), n=0..12); # _Johannes W. Meijer_, Jan 05 2017
%t A067624 Table[Abs[Det[Array[KroneckerDelta[#1 + 1, #2]*I &, {4*n, 4*n}] + Array[KroneckerDelta[#1 - 1, #2]*#1 &, {4*n, 4*n}]]], {n, 1, 20}] (* _John M. Campbell_, Jun 04 2011 *)
%t A067624 Table[2^(2 n) (2 n)!, {n, 0, 30}] (* _Vincenzo Librandi_, Feb 18 2018 *)
%o A067624 (Magma) [2^(2*n)*Factorial(2*n): n in [0..15]]; // _Vincenzo Librandi_, Feb 18 2018
%Y A067624 Cf. A000165.
%Y A067624 Appears in A162445, A061549 and A120738. - _Johannes W. Meijer_, Jul 06 2009
%K A067624 nonn
%O A067624 0,2
%A A067624 _Benoit Cloitre_, Feb 02 2002
%E A067624 More terms from _James Sellers_, Feb 11 2002