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A085157 Quintuple factorials, 5-factorials, n!!!!!, n!5. 23
1, 1, 2, 3, 4, 5, 6, 14, 24, 36, 50, 66, 168, 312, 504, 750, 1056, 2856, 5616, 9576, 15000, 22176, 62832, 129168, 229824, 375000, 576576, 1696464, 3616704, 6664896, 11250000, 17873856, 54286848, 119351232, 226606464, 393750000, 643458816 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The term "Quintuple factorial numbers" is also used for the sequences A008546, A008548, A052562, A047055, A047056 which have a different definition. The definition given here is the one commonly used.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

P. Luschny, Multifactorials

Eric Weisstein's World of Mathematics, Multifactorial

FORMULA

a(n) = 1 for n < 1, otherwise a(n) = n*a(n-5).

EXAMPLE

a(12) = 168 because 12*a(12-5) = 12*a(7) = 12*14 = 168.

MAPLE

a:= n-> `if`(n < 1, 1, n*a(n-5)) end proc; seq(a(n), n = 0..40); # G. C. Greubel, Aug 18 2019

MATHEMATICA

a[n_]:= If[n<1, 1, n*a[n-5]]; Table[a[n], {n, 0, 40}] (* G. C. Greubel, Aug 18 2019 *)

Table[Times@@Range[n, 1, -5], {n, 0, 40}] (* Harvey P. Dale, May 12 2020 *)

PROG

(PARI) a(n)=if(n<1, 1, n*a(n-5))

for(n=0, 50, print1(a(n), ", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 19 2006

(MAGMA)

b:= func< n | (n lt 6) select n else n*Self(n-5) >;

[1] cat [b(n): n in [1..40]]; // G. C. Greubel, Aug 18 2019

(Sage)

def a(n):

    if (n<1): return 1

    else: return n*a(n-5)

[a(n) for n in (0..40)] # G. C. Greubel, Aug 18 2019

(GAP)

a:= function(n)

    if n<1 then return 1;

    else return n*a(n-5);

    fi;

  end;

List([0..40], n-> a(n) ); # G. C. Greubel, Aug 18 2019

(Python)

def A085157(n):

    if n <= 0:

        return 1

    else:

        return n*A085157(n-5)

n = 0

while n <= 40:

    print(n, A085157(n))

    n = n+1 # A.H.M. Smeets, Aug 18 2019

CROSSREFS

Cf. n!:A000142, n!!:A006882, n!!!:A007661, n!!!!:A007662, n!!!!!!:A085158, 5-factorial primes: n!!!!!+1:A085148, n!!!!!-1:A085149.

Sequence in context: A084830 A116044 A116027 * A065637 A325805 A039061

Adjacent sequences:  A085154 A085155 A085156 * A085158 A085159 A085160

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, Jun 21 2003

STATUS

approved

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Last modified August 3 13:49 EDT 2020. Contains 336198 sequences. (Running on oeis4.)