A163086 Product of first n terms of A163085.

1, 1, 2, 24, 1728, 3732480, 161243136000, 975198486528000000, 412860031256494080000000000, 110116706384632080236544000000000000000, 7401233839469056679744633202278400000000000000000000

Offset: 0

Author

Peter Luschny, Jul 21 2009

Keywords

• nonn

Crossrefs

Cf. A056040, A163085, A055462, A000178.

Programs

Maple

a := proc(n) local i; mul(A163085(i),i=0..n) end;

Mathematica

b[0] = 1; b[n_] := b[n] = b[n-1] n! / Floor[n/2]!^2;
a[n_] := Product[b[k], {k, 0, n}];
Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Jul 11 2019 *)

Sage

def A163086(n):
    swing = lambda n: factorial(n)/factorial(n//2)^2
    return mul(swing(i+1)^(n-i) for i in (0..n))
[A163086(i) for i in (0..10)] # Peter Luschny, Sep 18 2012

Formula

a(n) = product_{i=0..n} A056040(i+1)^(n-i). - Peter Luschny, Sep 18 2012