A205958 -id:A205958 - cp's OEIS frontend

A230714 a(n) = lcm(1,2,...,n)*a(floor(n/2))^2 for n > 0, a(0) = 1.

1, 1, 2, 6, 48, 240, 2160, 15120, 1935360, 5806080, 145152000, 1596672000, 129330432000, 1681295616000, 82383485184000, 82383485184000, 2699542042509312000, 45892214722658304000, 413029932503924736000, 7847568717574569984000, 4904730448484106240000000

Offset: 0

Peter Luschny, Oct 28 2013

nonn

This sequence essentially documents the identity sqrt(A000142(n)*A205958(n)*A056040(n)*A180000(n)) = A003418(n)*a(floor(n/2)). Some interest derives from the fact that A056040 and A180000 can be computed by a structurally identical algorithm which can be used to compute A205958 and A000142, the latter being the fastest algorithm presently known to compute the factorial numbers. a(n) relates these numbers with lcm(1,2,3,...,n).

Michael De Vlieger, Table of n, a(n) for n = 0..351

Cf. A003418, A180000.

a := n -> `if`(n = 0, 1, lcm(seq(i,i=1..n))*a(floor(n/2))^2): seq(a(n),n=0..20);

Fold[Append[#1, Apply[LCM, Range@ #2] #1[[Floor[#2/2] + 1]]^2 ] &, {1}, Range@ 20] (* Michael De Vlieger, Mar 04 2018 *)

a(n)=lcm(vector(n,i,i))*if(n>3,a(n\2)^2,1) \\ Charles R Greathouse IV, Oct 31 2013

def A230714(n):
    return factorial(n)*A205958(n)
[A230714(n) for n in (0..20)]

a(n) = A205958(n)*n!.

cp's OEIS Frontend

A230714 a(n) = lcm(1,2,...,n)*a(floor(n/2))^2 for n > 0, a(0) = 1.

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