cp's OEIS Frontend

A214916 a(0) = a(1) = 1, a(n) = n! / a(n-2).

%I A214916 #33 Jun 06 2025 00:28:47
%S A214916 1,1,2,6,12,20,60,252,672,1440,5400,27720,88704,224640,982800,5821200,
%T A214916 21288960,61102080,300736800,1990850400,8089804800,25662873600,
%U A214916 138940401600,1007370302400,4465572249600,15397724160000,90311261040000,707173952284800,3375972620697600
%N A214916 a(0) = a(1) = 1, a(n) = n! / a(n-2).
%C A214916 a(n) is least k > a(n-1) such that k*a(n-2) is a factorial.
%C A214916 Two periodic subsets of these numbers appear in the coefficients of a series involved in a solution of a Riccati-type differential equation addressed by the Bernoulli brothers: z = 1 - x^4/12 + x^8/672 - x^12/88704 + ... = 1 - 2 * x^4/4! + 60 * x^8/8! - 5400 * x^12/12! + ... . See the MathOverflow question. - _Tom Copeland_, Jan 24 2017
%H A214916 Joerg Arndt, <a href="/A214916/b214916.txt">Table of n, a(n) for n = 0..100</a>
%H A214916 MathOverflow, <a href="http://mathoverflow.net/questions/260279/link-of-a-power-series-by-the-bernoullis-for-a-riccati-equation-to-zonotopes">Link of a power series by the Bernoulli brothers for a Riccati equation to zonotopes?</a>, a MathOverflow question by Tom Copeland, 2017.
%F A214916 a(0) = a(1) = 1, for n>=2, a(n) = n! / a(n-2).
%F A214916 a(n) = n!!!! * (n-1)!!!! = A007662(n) * A007662(n-1), for n >= 1. - _David Radcliffe_, Jun 05 2025
%o A214916 (Python)
%o A214916 import math
%o A214916 prpr = prev = 1
%o A214916 for n in range(2, 33):
%o A214916     print(prpr, end=', ')
%o A214916     cur = math.factorial(n) // prpr
%o A214916     prpr = prev
%o A214916     prev = cur
%o A214916 (Magma) [1] cat  [n le 2 select n  else  Factorial(n)  div  Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Jan 25 2017
%Y A214916 Cf. A214914, A214915, A214961, A214963, A007662.
%K A214916 nonn
%O A214916 0,3
%A A214916 _Alex Ratushnyak_, Aug 03 2012