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A111394 a(n) = product of first n integers not divisible by 3. 1
1, 2, 8, 40, 280, 2240, 22400, 246400, 3203200, 44844800, 717516800, 12197785600, 231757926400, 4635158528000, 101973487616000, 2345390215168000, 58634755379200000, 1524503639859200000, 42686101916057600000, 1237896955565670400000, 38374805622535782400000 (list; graph; refs; listen; history; text; internal format)
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 *)

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

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Last modified November 28 02:51 EST 2022. Contains 358406 sequences. (Running on oeis4.)