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
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
Programs
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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
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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
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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