A066459 Product of factorials of the digits of n.

1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 2, 2, 4, 12, 48, 240, 1440, 10080, 80640, 725760, 6, 6, 12, 36, 144, 720, 4320, 30240, 241920, 2177280, 24, 24, 48, 144, 576, 2880, 17280, 120960, 967680

Offset: 0

Author

Jason Earls, Jan 02 2002

Keywords

• base
• easy
• nonn

Examples

			a(24) = (2!) * (4!) = 2 * 24 = 48.
		

Links

• Harry J. Smith and Indranil Ghosh, Table of n, a(n) for n = 0..10000 (first 1001 terms from Harry J. Smith)
• Eric Weisstein's World of Mathematics, Factorial
• Index entries for sequences related to factorial numbers

Crossrefs

Cf. A000142, A034879 (iterated).

Programs

Haskell

import Data.List (unfoldr)
a066459 = product . map a000142 .
   unfoldr (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 10)
-- Reinhard Zumkeller, Oct 11 2011

Maple

A066459 := proc(n)
    local a,d;
    a := 1 ;
    for d in convert(n,base,10) do
        a := a*d! ;
    end do:
    a ;
end proc: # R. J. Mathar, Aug 07 2014

Mathematica

Table[Times@@(IntegerDigits[n]!),{n,0,50}] (* Harvey P. Dale, Oct 20 2024 *)

PARI

{ for (n=0, 1000, m=n; a=1; while (m>0, d=m%10; m=(m-d)/10; a*=d!); write("b066459.txt", n, " ", a) ) } \\ Harry J. Smith, Feb 15 2010

Python

import math
def A066459(n):
    s=1
    for i in str(n):
        s*=math.factorial(int(i))
    return s # Indranil Ghosh, Jan 11 2017

Formula

If n=10*q+r, (0 <= r < 10) then a(n) = (q+1+r)!*Sum_{k=0..r} (-1)^(q-k)*binomial(r,k)/(q+1+r-k). - Milan Janjic, Dec 14 2008