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A114790 Cumulative product of quintuple factorial A085157. 2
1, 1, 2, 6, 24, 120, 720, 10080, 241920, 8709120, 435456000, 28740096000, 4828336128000, 1506440871936000, 759246199455744000, 569434649591808000000, 601322989968949248000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..84

Eric Weisstein's World of Mathematics, Multifactorial.

FORMULA

a(n) = Product_{j=0..n} j!!!!!.

a(n) = Product_{[j=0..n} j!5.

a(n) = Product_{j=0..n} A085157(j).

a(n) = n!!!!! * a(n-1) where a(0) = 1, a(1) = 1 and n >= 2.

a(n) = n*(n-5)!!!!! * a(n-1) where a(0) = 1, a(1) = 1, a(2) = 2.

EXAMPLE

a(10) = 1!!!!! * 2!!!!! * 3!!!!! * 4!!!!! * 5!!!!! * 6!!!!! * 7!!!!! * 8!!!!! * 9!!!!! * 10!!!!! = 1 * 2 * 3 * 4 * 5 * 6 * 14 * 24 * 36 * 50 = 435456000 = 2^11 * 3^5 * 5^3 * 7.

MAPLE

b:= n-> `if`(n < 1, 1, n*b(n-5)); a:= n-> product(b(j), j = 0..n); seq(a(n), n = 0..20); # G. C. Greubel, Aug 21 2019

MATHEMATICA

b[n_]:= If[n<1, 1, n*b[n-5]]; a[n_]:= Product[b[j], {j, 0, n}]; Table[a[n], {n, 0, 20}] (* G. C. Greubel, Aug 21 2019 *)

PROG

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

vector(20, n, n--; prod(j=0, n, b(j)) ) \\ G. C. Greubel, Aug 21 2019

(MAGMA) b:= func< n | n eq 0 select 1 else (n lt 6) select n else n*Self(n-5) >;

[(&*[b(j): j in [0..n]]): n in [0..20]]; // G. C. Greubel, Aug 21 2019

(Sage)

@CachedFunction

def b(n):

    if (n<1): return 1

    else: return n*b(n-5)

[product(b(j) for j in (0..n)) for n in (0..20)] # G. C. Greubel, Aug 21 2019

(GAP)

b:= function(n)

    if n<1 then return 1;

    else return n*b(n-5);

    fi;

  end;

List([0..20], n-> Product([0..n], j-> b(j)) ); # G. C. Greubel, Aug 21 2019

CROSSREFS

Cf. A000178, A006882, A007662, A085157, A114347.

Sequence in context: A129655 A114796 A265086 * A352430 A292749 A351984

Adjacent sequences:  A114787 A114788 A114789 * A114791 A114792 A114793

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Feb 18 2006

STATUS

approved

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Last modified August 14 10:58 EDT 2022. Contains 356116 sequences. (Running on oeis4.)