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

1,2

Links

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

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

Example

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

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 *)

Prog

(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
(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

Crossrefs

Sequence in context: A296676 A281910 A180736 * A140363 A280921 A208962

Adjacent sequences: A111391 A111392 A111393 * A111395 A111396 A111397

Keyword

nonn

Author

Jon Perry, Nov 11 2005

Status

approved