A007662 -id:A007662 - cp's OEIS frontend

A329176 Numbers k such that k![4] - 128 is prime, where k![4] = A007662(k) = quadruple factorial.

11, 13, 17, 19, 25, 27, 29, 41, 47, 61, 75, 113, 181, 251, 287, 339, 521, 533, 573, 687, 739, 1015, 1243, 1811, 2073, 2851, 2939, 3421, 4055, 4211, 4477, 5219, 6151, 8851, 9251, 14219, 17123, 21703, 24313, 25053, 28811, 33065, 49305, 50775, 52693, 69805, 82077, 87771

Offset: 1

Robert Price, Nov 07 2019

nonn

a(49) > 10^5.

The first 5 primes associated with this sequence are: 103, 457, 9817, 65707, 5220997.

C. K. Caldwell, The Prime Glossary, multifactorial prime
C. Caldwell and H. Dubner (Eds): The top ten prime numbers: from the unpublished collections of R. Ondrejka (May 2001), Table 21 F, p. 75.
Ken Davis, Status of Search for Multifactorial Primes.
Joe McLean, Interesting Sources of Probable Primes

Cf. A007662, A283553.

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[1000], (x = MultiFactorial[#, 4] - 128; x > 0 && PrimeQ[x]) &]
Select[Range[10,90000],PrimeQ[Times@@Range[#,1,-4]-128]&] (* Harvey P. Dale, May 13 2022 *)

A329177 Numbers k such that k![4] - 256 is prime, where k![4] = A007662(k) = quadruple factorial.

Original entry on oeis.org

15, 17, 19, 21, 23, 25, 33, 39, 41, 43, 53, 63, 67, 73, 157, 167, 181, 195, 221, 327, 363, 419, 849, 861, 1233, 1265, 1599, 2413, 2515, 4009, 8291, 8475, 10685, 13957, 17453, 18409, 19117, 22739, 33313, 37861, 59703, 64983, 80697

Offset: 1

Robert Price, Nov 07 2019

nonn

a(44) > 10^5.

The first 5 primes associated with this sequence are: 3209, 9689, 65579, 208589, 1513949.

C. K. Caldwell, The Prime Glossary, multifactorial prime
C. Caldwell and H. Dubner (Eds): The top ten prime numbers: from the unpublished collections of R. Ondrejka (May 2001), Table 21 F, p. 75.
Ken Davis, Status of Search for Multifactorial Primes.
Joe McLean, Interesting Sources of Probable Primes

Cf. A007662, A283553.

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[1000], (x = MultiFactorial[#, 4] - 256; x > 0 && PrimeQ[x]) &]
Select[Range[10,1600],PrimeQ[Times@@Range[#,1,-4]-256]&] (* The program generates the first 27 terms of the sequence. To generate more, increase the second Range constant but the program may take a long time to run. *) (* Harvey P. Dale, Aug 01 2022 *)

A329183 Numbers k such that k![4] - 512 is prime, where k![4] = A007662(k) = quadruple factorial.

Original entry on oeis.org

13, 15, 17, 19, 21, 23, 25, 35, 39, 47, 67, 71, 89, 93, 113, 153, 163, 185, 201, 267, 427, 491, 871, 1645, 3075, 3351, 3435, 5385, 7893, 10649, 15597, 44641, 50039, 57269, 67647, 83061, 89717

Offset: 1

Robert Price, Nov 07 2019

nonn

a(38) > 10^5.

The first 5 primes associated with this sequence are: 73, 2953, 9433, 65323, 208333.

C. K. Caldwell, The Prime Glossary, multifactorial prime
C. Caldwell and H. Dubner (Eds): The top ten prime numbers: from the unpublished collections of R. Ondrejka (May 2001), Table 21 F, p. 75.
Ken Davis, Status of Search for Multifactorial Primes.
Joe McLean, Interesting Sources of Probable Primes

Cf. A007662, A283553.

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[1000], (x = MultiFactorial[#, 4] - 512; x > 0 && PrimeQ[x]) &]

A329184 Numbers k such that k![4] - 1024 is prime, where k![4] = A007662(k) = quadruple factorial.

Original entry on oeis.org

15, 19, 21, 25, 27, 33, 47, 51, 55, 85, 95, 153, 163, 187, 191, 315, 335, 363, 375, 419, 433, 669, 873, 1097, 1113, 1235, 1819, 1969, 2043, 2391, 2493, 3639, 4433, 5527, 6423, 9441, 14099, 24607, 27057, 62271, 98079

Offset: 1

Robert Price, Nov 07 2019

nonn

a(42) > 10^5.

The first 5 primes associated with this sequence are: 2441, 64811, 207821, 5220101, 40882511.

C. K. Caldwell, The Prime Glossary, multifactorial prime
C. Caldwell and H. Dubner (Eds): The top ten prime numbers: from the unpublished collections of R. Ondrejka (May 2001), Table 21 F, p. 75.
Ken Davis, Status of Search for Multifactorial Primes.
Joe McLean, Interesting Sources of Probable Primes

Cf. A007662, A283553.

MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[1000], (x = MultiFactorial[#, 4] - 1024; x > 0 && PrimeQ[x]) &]

A007661 Triple factorial numbers a(n) = n!!!, defined by a(n) = n*a(n-3), a(0) = a(1) = 1, a(2) = 2. Sometimes written n!3.

Original entry on oeis.org

1, 1, 2, 3, 4, 10, 18, 28, 80, 162, 280, 880, 1944, 3640, 12320, 29160, 58240, 209440, 524880, 1106560, 4188800, 11022480, 24344320, 96342400, 264539520, 608608000, 2504902400, 7142567040, 17041024000, 72642169600, 214277011200, 528271744000, 2324549427200

Offset: 0

N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v

The triple factorial of a positive integer n is the product of the positive integers <= n that have the same residue modulo 3 as n. - Peter Luschny, Jun 23 2011

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. Spanier and K. B. Oldham, An Atlas of Functions, Hemisphere, NY, 1987, p. 23.

T. D. Noe, Table of n, a(n) for n = 0..200
Shyam Sunder Gupta, Fascinating Factorials, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 16, 411-442.
Eric Weisstein's World of Mathematics, Multifactorial.

Union of A007559, A008544 and A032031.
Cf. A000142, A006882 (= A001147 union A000165), A007662 (= union of A007696, A001813, A008545 and A047053), A085157, A085158.
Cf. A008585, A016777, A016789, A161474, A288055.

a:= function(n)
    if n<3 then return Fibonacci(n+1);
    else return n*a(n-3);
    fi;
  end;
List([0..30], n-> a(n) ); # G. C. Greubel, Aug 21 2019

a007661 n k = a007661_list !! n
a007661_list = 1 : 1 : 2 : zipWith (*) a007661_list [3..]
-- Reinhard Zumkeller, Sep 20 2013

I:=[1,1,2];[n le 3 select I[n] else (n-1)*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Nov 27 2015

A007661 := n -> mul(k, k = select(k -> k mod 3 = n mod 3, [$1 .. n])): seq(A007661(n), n = 0 .. 29);  # Peter Luschny, Jun 23 2011

multiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*multiFactorial[n - k, k]]]; Array[ multiFactorial[#, 3] &, 30, 0] (* Robert G. Wilson v, Apr 23 2011 *)
RecurrenceTable[{a[0]==a[1]==1,a[2]==2,a[n]==n*a[n-3]},a,{n,30}] (* Harvey P. Dale, May 17 2012 *)
Table[With[{q = Quotient[n + 2, 3]}, 3^q q! Binomial[n/3, q]], {n, 0, 30}] (* Jan Mangaldan, Mar 21 2013 *)
a[ n_] := With[{m = Mod[n, 3, 1], q = 1 + Quotient[n, 3, 1]}, If[n < 0, 0, 3^q Pochhammer[m/3, q]]]; (* Michael Somos, Feb 24 2019 *)
Table[Times@@Range[n,1,-3],{n,0,30}] (* Harvey P. Dale, Sep 12 2020 *)

A007661(n,d=3)=prod(i=0,(n-1)\d,n-d*i) \\ M. F. Hasler, Feb 16 2008

def a(n):
    if (n<3): return fibonacci(n+1)
    else: return n*a(n-3)
[a(n) for n in (0..30)] # G. C. Greubel, Aug 21 2019

a(n) = Product_{i=0..floor((n-1)/3)} (n-3*i). - M. F. Hasler, Feb 16 2008
a(n) ~ c * n^(n/3+1/2)/exp(n/3), where c = sqrt(2*Pi/3) if n=3*k, c = sqrt(2*Pi)*3^(1/6) / Gamma(1/3) if n=3*k+1, c = sqrt(2*Pi)*3^(-1/6) / Gamma(2/3) if n=3*k+2. - Vaclav Kotesovec, Jul 29 2013
a(3*n) = A032031(n); a(3*n+1) = A007559(n+1); a(3*n+2) = A008544(n+1). - Reinhard Zumkeller, Sep 20 2013
0 = a(n)*(a(n+1) -a(n+4)) +a(n+1)*a(n+3) for all n>=0. - Michael Somos, Feb 24 2019
Sum_{n>=0} 1/a(n) = A288055. - Amiram Eldar, Nov 10 2020

A085158 Sextuple factorials, 6-factorials, n!!!!!!, n!6.

Original entry on oeis.org

1, 1, 2, 3, 4, 5, 6, 7, 16, 27, 40, 55, 72, 91, 224, 405, 640, 935, 1296, 1729, 4480, 8505, 14080, 21505, 31104, 43225, 116480, 229635, 394240, 623645, 933120, 1339975, 3727360, 7577955, 13404160, 21827575, 33592320, 49579075, 141639680

Offset: 0

Hugo Pfoertner, Jun 21 2003

nonn

The term "Sextuple factorial numbers" is also used for the sequences A008542, A008543, A011781, A047058, A047657, A049308, which have a different definition. The definition given here is the one commonly used.

			a(14) = 224 because 14*a(14-6) = 14*a(8) = 14*16 = 224.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Multifactorial.

Cf. n!:A000142, n!!:A006882, n!!!:A007661, n!!!!:A007662, n!!!!!:A085157, 6-factorial primes: n!!!!!!+1:A085150, n!!!!!!-1:A051592.

Cf. A288093.

a:= function(n)
    if n<1 then return 1;
    else return n*a(n-6);
    fi;
  end;
List([0..40], n-> a(n) ); # G. C. Greubel, Aug 21 2019

b:=func< n | n le 6 select n else n*Self(n-6) >;
[1] cat [b(n): n in [1..40]]; // G. C. Greubel, Aug 21 2019

a:= n-> `if`(n<1, 1, n*a(n-6)); seq(a(n), n=0..40); # G. C. Greubel, Aug 21 2019

Table[Times@@Range[n,1,-6],{n,0,40}] (* Harvey P. Dale, Aug 10 2019 *)

a(n)=if(n<1, 1, n*a(n-6));
vector(40, n, n--; a(n) ) \\ G. C. Greubel, Aug 21 2019

def a(n):
    if (n<1): return 1
    else: return n*a(n-6)
[a(n) for n in (0..40)] # G. C. Greubel, Aug 21 2019

a(n)=1 for n < 1, otherwise a(n) = n*a(n-6).

Sum_{n>=0} 1/a(n) = A288093. - Amiram Eldar, Nov 10 2020

A008542 Sextuple factorial numbers: Product_{k=0..n-1} (6*k+1).

Original entry on oeis.org

1, 1, 7, 91, 1729, 43225, 1339975, 49579075, 2131900225, 104463111025, 5745471106375, 350473737488875, 23481740411754625, 1714167050058087625, 135419196954588922375, 11510631741140058401875, 1047467488443745314570625, 101604346379043295513350625

Offset: 0

Joe Keane (jgk(AT)jgk.org)

nonn

a(n), n>=1, enumerates increasing heptic (7-ary) trees with n vertices. - Wolfdieter Lang, Sep 14 2007; see a D. Callan comment on A007559 (number of increasing quarterny trees).

Vincenzo Librandi, Table of n, a(n) for n = 0..300
Index entries for sequences related to factorial numbers.

Cf. A085158, A034689, A034723, A034724, A034787, A034788, A004993, A047058, A047657, A051151.

Cf. k-fold factorials: A000142, A001147 (and A000165, A006882), A007559 (and A032031, A008544, A007661), A007696 (and A001813, A008545, A047053, A007662), A008548 (and A052562, A047055, A085157), A045754 (and A084947, A114799), A045755.

List([0..20], n-> Product([0..n-1], k-> (6*k+1) )); # G. C. Greubel, Aug 17 2019

[1] cat [(&*[(6*k+1): k in [0..n-1]]): n in [1..20]]; // G. C. Greubel, Aug 17 2019

a := n -> mul(6*k+1, k=0..n-1);
G(x):=(1-6*x)^(-1/6): f[0]:=G(x): for n from 1 to 29 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=0..15); # Zerinvary Lajos, Apr 03 2009

Table[Product[(6*k+1), {k,0,n-1}], {n,0,20}] (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008, modified by G. C. Greubel, Aug 17 2019 *)
FoldList[Times, 1, 6Range[0, 20] + 1] (* Vincenzo Librandi, Jun 10 2013 *)
Table[6^n*Pochhammer[1/6, n], {n,0,20}] (* G. C. Greubel, Aug 17 2019 *)

a(n)=prod(k=1,n-1,6*k+1) \\ Charles R Greathouse IV, Jul 19 2011

[product((6*k+1) for k in (0..n-1)) for n in (0..20)] # G. C. Greubel, Aug 17 2019

E.g.f.: (1-6*x)^(-1/6).
a(n) ~ 2^(1/2)*Pi^(1/2)*Gamma(1/6)^-1*n^(-1/3)*6^n*e^-n*n^n*{1 + 1/72*n^-1 - ...}. - Joe Keane (jgk(AT)jgk.org), Nov 24 2001
a(n) = Sum_{k=0..n} (-6)^(n-k)*A048994(n, k). - Philippe Deléham, Oct 29 2005
G.f.: 1+x/(1-7x/(1-6x/(1-13x/(1-12x/(1-19x/(1-18x/(1-25x/(1-24x/(1-... (continued fraction). - Philippe Deléham, Jan 08 2012
a(n) = (-5)^n*Sum_{k=0..n} (6/5)^k*s(n+1,n+1-k), where s(n,k) are the Stirling numbers of the first kind, A048994. - Mircea Merca, May 03 2012
G.f.: 1/Q(0) where Q(k) = 1 - x*(6*k+1)/(1 - x*(6*k+6)/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Mar 20 2013
a(n) = A085158(6*n-5). - M. F. Hasler, Feb 23 2018
D-finite with recurrence: a(n) +(-6*n+5)*a(n-1)=0. - R. J. Mathar, Jan 17 2020
Sum_{n>=0} 1/a(n) = 1 + (e/6^5)^(1/6)*(Gamma(1/6) - Gamma(1/6, 1/6)). - Amiram Eldar, Dec 18 2022

A045754 7-fold factorials: a(n) = Product_{k=0..n-1} (7*k+1).

Original entry on oeis.org

1, 1, 8, 120, 2640, 76560, 2756160, 118514880, 5925744000, 337767408000, 21617114112000, 1534815101952000, 119715577952256000, 10175824125941760000, 936175819586641920000, 92681406139077550080000, 9824229050742220308480000, 1110137882733870894858240000

Offset: 0

Wolfdieter Lang

nonn

G. C. Greubel, Table of n, a(n) for n = 0..338
Index entries for sequences related to factorial numbers.

Cf. k-fold factorials: A000142, A001147 (and A000165, A006882), A007559 (and A032031, A008544, A007661), A007696 (and A001813, A008545, A047053, A007662), A008548 (and A052562, A047055, A085157), A008542 (and A085158), A045755.
See also A113134.
Unsigned row sums of triangle A051186 (scaled Stirling1).
First column of triangle A132056 (S2(8)).
Cf. A114799, A084947, A144739, A144827, A147585, A049209, A051188.

List([0..20], n-> Product([0..n-1], k-> 7*k+1) ); # G. C. Greubel, Aug 21 2019

[1] cat [&*[7*j+1: j in [0..n-1]]: n in [1..20]]; // G. C. Greubel, Aug 21 2019

f := n->product( (7*k+1), k=0..(n-1));
G(x):=(1-7*x)^(-1/7): f[0]:=G(x): for n from 1 to 29 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=0..14); # Zerinvary Lajos, Apr 03 2009

FoldList[Times, 1, 7Range[0, 20] + 1] (* Harvey P. Dale, Jan 21 2013 *)

PARI
```
a(n)=prod(k=0,n-1,7*k+1)
```

[7^n*rising_factorial(1/7, n) for n in (0..20)] # G. C. Greubel, Aug 21 2019

a(n) = Sum_{k=0..n} (-7)^(n-k)*A048994(n, k), where A048994 = Stirling-1 numbers.
E.g.f.: (1-7*x)^(-1/7).
G.f.: 1/(1-x/(1-7*x/(1-8*x/(1-14*x/(1-15*x/(1-21*x/(1-22*x/(1-... (continued fraction). - Philippe Deléham, Jan 08 2012
a(n) = (-6)^n*Sum_{k=0..n} (7/6)^k*s(n+1,n+1-k), where s(n,k) are the Stirling numbers of the first kind, A048994. - Mircea Merca, May 03 2012
G.f.: 1/G(0), where G(k)= 1 - x*(7*k+1)/(1 - x*(7*k+7)/G(k+1)); (continued fraction). - Sergei N. Gladkovskii, Jun 05 2013
G.f.: G(0)/2, where G(k)= 1 + 1/(1 - x*(7*k+1)/(x*(7*k+1) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 05 2013
a(n) = 7^n * Gamma(n + 1/7) / Gamma(1/7). - Artur Jasinski, Aug 23 2016
a(n) = A114799(7n-6). - M. F. Hasler, Feb 23 2018
D-finite with recurrence: a(n) +(-7*n+6)*a(n-1)=0. - R. J. Mathar, Jan 17 2020
Sum_{n>=0} 1/a(n) = 1 + (e/7^6)^(1/7)*(Gamma(1/7) - Gamma(1/7, 1/7)). - Amiram Eldar, Dec 19 2022

Additional comments from Philippe Deléham and Paul D. Hanna, Oct 29 2005
Edited by N. J. A. Sloane, Oct 16 2008 at the suggestion of M. F. Hasler, Oct 14 2008
Corrected by Zerinvary Lajos, Apr 03 2009

A085157 Quintuple factorials, 5-factorials, n!!!!!, n!5.

Original entry on oeis.org

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

Offset: 0

Hugo Pfoertner, Jun 21 2003

nonn

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.

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

G. C. Greubel, Table of n, a(n) for n = 0..1000
Peter Luschny, Multifactorials
Eric Weisstein's World of Mathematics, Multifactorial.

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

Cf. A288092.

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

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

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

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 *)

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

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

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

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

Sum_{n>=0} 1/a(n) = A288092. - Amiram Eldar, Nov 10 2020

A114800 Octuple factorial, 8-factorial, n!8, n!!!!!!!!.

Original entry on oeis.org

1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 20, 33, 48, 65, 84, 105, 128, 153, 360, 627, 960, 1365, 1848, 2415, 3072, 3825, 9360, 16929, 26880, 39585, 55440, 74865, 98304, 126225, 318240, 592515, 967680, 1464645, 2106720, 2919735, 3932160, 5175225, 13366080

Offset: 0

Jonathan Vos Post, Feb 18 2006

			a(10) = 10 * a(10-8) = 10 * a(2) = 10 * 2 = 20.
a(20) = 20 * a(20-8) = 20 * a(12) = 20 * (12*a(12-8)) = 20 * 12 * a(4) = 20 * 12 * 4 = 960.
a(30) = 30 * a(30-8) = 30 * a(22) = 30 * (22*a(22-8)) = 30 * 22 * a(14) = 30 * 22 * (14*a(14-8)) = 30 * 22 * 14 * 6 = 55440.

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Multifactorial.

Cf. A000142, A006882, A007661, A007662, A085157, A085158, A288095.

a:= function(n)
    if n<1 then return 1;
    else return n*a(n-8);
    fi;
  end;
List([0..50], n-> a(n) ); # G. C. Greubel, Aug 21 2019

b:=func< n | n le 8 select n else n*Self(n-8) >;
[1] cat [b(n): n in [1..50]]; // G. C. Greubel, Aug 21 2019

A114800 := proc(n)
    option remember;
    if n < 1 then
        1;
    else
        n*procname(n-8) ;
    end if;
end proc:
seq(A114800(n),n=0..40) ; # R. J. Mathar, Jun 23 2014

Table[Times@@Range[n,1,-8],{n,0,50}] (* Harvey P. Dale, Feb 17 2018 *)

a(n)=if(n<1, 1, n*a(n-8));
vector(50, n, n--; a(n) ) \\ G. C. Greubel, Aug 21 2019

def a(n):
    if (n<1): return 1
    else: return n*a(n-8)
[a(n) for n in (0..50)] # G. C. Greubel, Aug 21 2019

a(n) = 1 for n<1, else a(n) = n*a(n-8).

Sum_{n>=0} 1/a(n) = A288095. - Amiram Eldar, Nov 10 2020

cp's OEIS Frontend

A329176 Numbers k such that k![4] - 128 is prime, where k![4] = A007662(k) = quadruple factorial.

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A329177 Numbers k such that k![4] - 256 is prime, where k![4] = A007662(k) = quadruple factorial.

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A329183 Numbers k such that k![4] - 512 is prime, where k![4] = A007662(k) = quadruple factorial.

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A329184 Numbers k such that k![4] - 1024 is prime, where k![4] = A007662(k) = quadruple factorial.

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A007661 Triple factorial numbers a(n) = n!!!, defined by a(n) = n*a(n-3), a(0) = a(1) = 1, a(2) = 2. Sometimes written n!3.

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A085158 Sextuple factorials, 6-factorials, n!!!!!!, n!6.

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A008542 Sextuple factorial numbers: Product_{k=0..n-1} (6*k+1).

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