A248812 Repeated terms of (2n)! (A010050).

1, 1, 2, 2, 24, 24, 720, 720, 40320, 40320, 3628800, 3628800, 479001600, 479001600, 87178291200, 87178291200, 20922789888000, 20922789888000, 6402373705728000, 6402373705728000, 2432902008176640000, 2432902008176640000, 1124000727777607680000

Offset: 0

Author

Wesley Ivan Hurt, Oct 16 2014

Keywords

• nonn
• easy

Comments

For n>1, a(n) is the product of the smallest parts in the partitions of 4*floor(n/2) = A168273(n) into two parts.

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A000142, A052928, A010050, A168273, A211374.

Programs

Magma

[Factorial(2*Floor(n/2)) : n in [0..20]];

Maple

A248812:=n->(2*floor(n/2))!: seq(A248812(n), n=0..20);

Mathematica

Table[(2*Floor[n/2])!, {n, 0, 20}]

Formula

a(n) = ( 2*floor(n/2) )! = A000142(A052928(n)).

a(2n) = a(2n+1) = A010050(n) = A211374(2n-1).

E.g.f.: log((1+x)/(1-x))/2+1/(1-x^2). - Robert Israel, Oct 19 2014