A111394 a(n) = product of first n integers not divisible by 3.

1, 2, 8, 40, 280, 2240, 22400, 246400, 3203200, 44844800, 717516800, 12197785600, 231757926400, 4635158528000, 101973487616000, 2345390215168000, 58634755379200000, 1524503639859200000, 42686101916057600000, 1237896955565670400000, 38374805622535782400000

Offset: 1

Author

Jon Perry, Nov 11 2005

Keywords

• nonn

Examples

			a(5) = 1*2*4*5*7 = 280.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..160

Programs

Maple

a:= proc(n) a(n):= `if`(n=1, 1, (3*iquo(n, 2)-(-1)^n)*a(n-1)) end:
seq (a(n), n=1..25);  # Alois P. Heinz, Oct 03 2012

Mathematica

a[n_] := ((3*n-Mod[n, 2])/2)!/(3^((n-Mod[n, 2])/2)*((n-Mod[n, 2])/2)!); Table[a[n], {n, 1, 21}] (* Jean-François Alcover, Feb 25 2014 *)
FoldList[Times,Table[If[Divisible[n,3],Nothing,n],{n,40}]] (* Harvey P. Dale, Feb 28 2023 *)

PARI

{a(n)=local(A,G=sum(k=0,n,binomial(3*k,k)/(2*k+1)*x^k +x*O(x^n))); A=1/(1-x*subst(G,x,x^2/3))-1; n!*polcoeff(A,n)} \\ Paul D. Hanna, Jan 04 2014

PARI

{a(n)=local(A=x); for(i=0, n, A=intformal((1+A)^3*subst(1+A, x,-x +x*O(x^n))^1 +x*O(x^n) )); n!*polcoeff(A, n)} \\ Paul D. Hanna, Jan 04 2014

Sage

def Gauss_factorial(N, n): return mul(j for j in (1..N) if gcd(j, n) == 1)
def A111394_list(n): return sorted(set([Gauss_factorial(j, 3) for j in (1..n)]))
A111394_list(28) # Peter Luschny, Oct 01 2012

Formula

Let b(n) = n!/(3^floor(n/3)*floor(n/3)!) then a(n) = b(3*floor(n/2)+(-1)^(n+1)). # formula corrected Peter Luschny, Oct 03 2012

E.g.f.: 1/(1 - x*G(x^2/3)) - 1 where G(x) = 1 + x*G(x)^3 is the g.f. of A001764. - Paul D. Hanna, Jan 04 2014

E.g.f. A(x) satisfies: A'(x) = (1 + A(x))^3 * (1 + A(-x)). - Paul D. Hanna, Jan 04 2014