A007662 -id:A007662 - cp's OEIS frontend

A114799 Septuple factorial, 7-factorial, n!7, n!!!!!!!, a(n) = n*a(n-7) if n > 1, else 1.

1, 1, 2, 3, 4, 5, 6, 7, 8, 18, 30, 44, 60, 78, 98, 120, 288, 510, 792, 1140, 1560, 2058, 2640, 6624, 12240, 19800, 29640, 42120, 57624, 76560, 198720, 379440, 633600, 978120, 1432080, 2016840, 2756160, 7352640, 14418720, 24710400, 39124800

Offset: 0

Jonathan Vos Post, Feb 18 2006

Many of the terms yield multifactorial primes a(n) + 1, e.g.: a(2) + 1 = 3, a(4) + 1 = 5, a(6) + 1 = 7, a(9) + 1 = 19, a(10) + 1 = 31, a(12) + 1 = 61, a(13) + 1 = 79, a(24) + 1 = 12241, a(25) + 1 = 19801, a(26) + 1 = 29641, a(29) + 1 = 76561, a(31) + 1 = 379441, a(35) + 1 = 2016841, a(36) + 1 = 2756161, ...

Equivalently, product of all positive integers <= n congruent to n (mod 7). - M. F. Hasler, Feb 23 2018

			a(40) = 40 * a(40-7) = 40 * a(33) = 40 * (33*a(26)) = 40 * 33 * (26*a(19)) = 40 * 33 * 26 * (19*a(12)) = 40 * 33 * 26 * 19 * (12*a(5)) = 40 * 33 * 26 * 19 * 12 5 = 39124800.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Multifactorial.
Index entries for sequences related to factorial numbers

Cf. A045754, A084947, A288094.

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), A085158 (and A008542, A047058, A047657), A045755.

a:= function(n)
    if n<1 then return 1;
    else return n*a(n-7);
    fi;
  end;
List([0..40], n-> a(n) ); # G. C. Greubel, Aug 20 2019

b:= func< n | (n lt 8) select n else n*Self(n-7) >;
[1] cat [b(n): n in [1..40]]; // G. C. Greubel, Aug 20 2019

A114799 := proc(n)
    option remember;
    if n < 1 then
        1;
    else
        n*procname(n-7) ;
    end if;
end proc:
seq(A114799(n),n=0..40) ; # R. J. Mathar, Jun 23 2014
A114799 := n -> product(n-7*k,k=0..(n-1)/7); # M. F. Hasler, Feb 23 2018

a[n_]:= If[n<1, 1, n*a[n-7]]; Table[a[n], {n,0,40}] (* G. C. Greubel, Aug 20 2019 *)

A114799(n,k=7)=prod(j=0,(n-1)\k,n-j*k) \\ M. F. Hasler, Feb 23 2018

def a(n):
    if (n<1): return 1
    else: return n*a(n-7)
[a(n) for n in (0..40)] # G. C. Greubel, Aug 20 2019

a(n) = 1 for n <= 1, else a(n) = n*a(n-7).

Sum_{n>=0} 1/a(n) = A288094. - Amiram Eldar, Nov 10 2020

Edited by M. F. Hasler, Feb 23 2018

A114806 Nonuple factorial, 9-factorial, n!9, n!!!!!!!!!.

Original entry on oeis.org

1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 22, 36, 52, 70, 90, 112, 136, 162, 190, 440, 756, 1144, 1610, 2160, 2800, 3536, 4374, 5320, 12760, 22680, 35464, 51520, 71280, 95200, 123760, 157464, 196840, 484880, 884520, 1418560, 2112320, 2993760, 4093600

Offset: 0

Jonathan Vos Post, Feb 19 2006

			a(10) = 10 * a(10-9) = 10 * a(1) = 10 * 1 = 10.
a(20) = 20 * a(20-9) = 20 * a(11) = 20 * (11*a(11-9)) = 20 * 11 * a(2) = 20 * 11 * 2 = 440.
a(30) = 30 * a(30-9) = 30 * a(21) = 30 * (21*a(21-9)) = 30 * 21 * a(12) = 30 * 21 * (12*a(12-9)) = 30 * 21 * 12 * 3 = 22680.

Robert Israel, Table of n, a(n) for n = 0..2955
Eric Weisstein's World of Mathematics, Multifactorial.

Cf. A000142, A006882, A007661, A007662, A085157, A085158, A288096.

a:= function(n)
    if n<1 then return 1;
    else return n*a(n-9);
    fi;
  end;
List([0..50], n-> a(n) ); # G. C. Greubel, Aug 21 2019

b:=func< n | n le 9 select n else n*Self(n-9) >;
[1] cat [b(n): n in [1..50]]; // G. C. Greubel, Aug 21 2019

f:= proc(n) option remember;
n*procname(n-9)
end proc:
f(0):= 1: for n from 1 to 8 do f(n):= n od:
map(f, [$0..100]); # Robert Israel, Jun 21 2019

NFactorialM[n_, m_] := Block[{k = n, p = Max[1, n]}, While[k > m, k -= m; p *= k]; p]; Array[ NFactorialM[#, 9] &, 44, 0] (* Robert G. Wilson v, May 10 2011 *)
a[n_]:= a[n]= If[n<1, 1, n*a[n-9]]; Table[a[n], {n,0,50}] (* G. C. Greubel, Aug 21 2019 *)
Table[Times@@Range[n,1,-9],{n,0,50}] (* Harvey P. Dale, Nov 13 2021 *)

a(n)=if(n<1, 1, n*a(n-9));
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-9)
[a(n) for n in (0..50)] # G. C. Greubel, Aug 21 2019

D-finite with recurrence: a(0) = 1, a(n) = n for 1 <= n <= 9, a(n) = n*a(n-9) for n >= 10.
From Robert Israel, Jun 21 2019: (Start)
a(9*m) = 9^m*m!.
a(9*m+k) = 9^m*(9*m+k)*Gamma(m+k/9)/Gamma(k/9) for 1 <= k <= 8. (End)
Sum_{n>=0} 1/a(n) = A288096. - Amiram Eldar, Nov 10 2020

A085146 Numbers k such that k!!!! + 1 is prime.

Original entry on oeis.org

0, 1, 2, 4, 6, 18, 38, 56, 94, 118, 148, 286, 1358, 1480, 1514, 2680, 2846, 4078, 4288, 5612, 5680, 6440, 6586, 14614, 30972, 31690, 54406

Offset: 1

Hugo Pfoertner, Jun 25 2003

The search for multifactorial primes started by Ray Ballinger is now continued by a team of volunteers on the website of Ken Davis (see link).

Ken Davis, Status of Search for Multifactorial Primes.
Ken Davis, Results for n!4+1.

Cf. A007662 (quadruple factorials), A085147.

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008

A288091 Decimal expansion of m(4) = Sum_{n>=0} 1/n!!!!, the 4th reciprocal multifactorial constant.

Original entry on oeis.org

3, 4, 8, 5, 9, 4, 4, 9, 7, 7, 4, 5, 3, 5, 5, 7, 7, 4, 5, 2, 1, 8, 8, 0, 9, 0, 4, 4, 0, 4, 6, 4, 0, 4, 7, 9, 5, 0, 9, 2, 6, 8, 2, 3, 2, 0, 8, 8, 1, 9, 6, 9, 4, 0, 7, 6, 4, 7, 2, 4, 9, 9, 9, 8, 1, 3, 1, 6, 1, 3, 1, 7, 2, 2, 9, 0, 0, 5, 6, 6, 2, 9, 6, 4, 0, 2, 2, 1, 4, 4, 6, 9, 7, 5, 9, 8, 6, 0, 1, 8, 6, 8, 5, 9

Offset: 1

Jean-François Alcover, Jun 05 2017

			3.485944977453557745218809044046404795092682320881969407647249998...

G. C. Greubel, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Reciprocal Multifactorial Constant

Cf. A007662 (n!!!!), A143280 (m(2)), A288055 (m(3)), this sequence (m(4)), A288092 (m(5)), A288093 (m(6)), A288094 (m(7)), A288095 (m(8)), A288096 (m(9)).

SetDefaultRealField(RealField(100)); (1/4)*Exp(1/4)*(4 + Sqrt(2)* Gamma(1/4, 1/4) + 2*Gamma(1/2, 1/4) + 2*Sqrt(2)*Gamma(3/4, 1/4)) // G. C. Greubel, Mar 28 2019

m[4] = (1/4)*E^(1/4)*(4 + Sqrt[2]*(Gamma[1/4] - Gamma[1/4, 1/4]) + 2*(Sqrt[Pi] - Gamma[1/2, 1/4]) + 2*Sqrt[2]*(Gamma[3/4] - Gamma[3/4, 1/4])); RealDigits[m[4], 10, 104][[1]]

default(realprecision, 100); (1/4)*exp(1/4)*(4+sqrt(2)*(gamma(1/4) - incgam(1/4, 1/4))+2*(sqrt(Pi) -incgam(1/2, 1/4))+2*sqrt(2)*(gamma(3/4) - incgam(3/4, 1/4))) \\ G. C. Greubel, Mar 28 2019

numerical_approx((1/4)*exp(1/4)*(4 + sqrt(2)*(gamma(1/4) - gamma_inc(1/4, 1/4)) + 2*(sqrt(pi) - gamma_inc(1/2, 1/4)) + 2*sqrt(2)*(gamma(3/4) - gamma_inc(3/4, 1/4))), digits=100) # G. C. Greubel, Mar 28 2019

m(k) = (1/k)*exp(1/k)*(k + Sum_{j=1..k-1} k^(j/k)*(gamma(j/k) - gamma(j/k, 1/k))) where gamma(x) is the Euler gamma function and gamma(a,x) the incomplete gamma function.

A288327 Decuple factorial, 10-factorial, n!10, n!!!!!!!!!!.

Original entry on oeis.org

1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 24, 39, 56, 75, 96, 119, 144, 171, 200, 231, 528, 897, 1344, 1875, 2496, 3213, 4032, 4959, 6000, 7161, 16896, 29601, 45696, 65625, 89856, 118881, 153216, 193401, 240000, 293601, 709632, 1272843, 2010624, 2953125, 4133376

Offset: 0

Robert Price, Jun 07 2017

			a(13) = 13 * 3 * 1 = 39.

Robert Price, Table of n, a(n) for n = 0..803
Eric Weisstein's World of Mathematics, Multifactorial.

Cf. A006852, A007661, A007662, A085157, A085158, A114799, A114800, A114806, A342033.

a:= function(n)
    if n<1 then return 1;
    else return n*a(n-10);
    fi;
  end;
List([0..50], n-> a(n) ); # G. C. Greubel, Aug 22 2019

b:=func< n | n le 10 select n else n*Self(n-10) >;
[1] cat [b(n): n in [1..50]]; // G. C. Greubel, Aug 22 2019

a:= n-> `if`(n<1, 1, n*a(n-10)); seq(a(n), n=0..50); # G. C. Greubel, Aug 22 2019

MultiFactorial[n_, k_]:=If[n<1, 1 ,n*MultiFactorial[n-k, k]];
Table[MultiFactorial[i, 10], {i, 0, 100}]
Table[Times@@Range[n,1,-10],{n,0,50}] (* Harvey P. Dale, Aug 11 2019 *)

a(n)=if(n<1, 1, n*a(n-10));
vector(40, n, n--; a(n) ) \\ G. C. Greubel, Aug 22 2019

def a(n):
    if (n<1): return 1
    else: return n*a(n-10)
[a(n) for n in (0..50)] # G. C. Greubel, Aug 22 2019

a(n)=1 for n < 1, otherwise a(n) = n*a(n-10).

Sum_{n>=0} 1/a(n) = A342033. - Amiram Eldar, May 23 2022

A129116 Multifactorial array: A(k,n) = k-tuple factorial of n, for positive n, read by ascending antidiagonals.

Original entry on oeis.org

1, 1, 2, 1, 2, 6, 1, 2, 3, 24, 1, 2, 3, 8, 120, 1, 2, 3, 4, 15, 720, 1, 2, 3, 4, 10, 48, 5040, 1, 2, 3, 4, 5, 18, 105, 40320, 1, 2, 3, 4, 5, 12, 28, 384, 362880, 1, 2, 3, 4, 5, 6, 21, 80, 945, 3628800, 1, 2, 3, 4, 5, 6, 14, 32, 162, 3840, 39916800, 1, 2, 3, 4, 5, 6, 7, 24, 45, 280, 10395, 479001600

Offset: 1

Jonathan Vos Post, May 24 2007

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. This problem exists for the other rows as well. "n!2" = n!!, "n!3" = n!!!, "n!4" = n!!!!, etcetera. Main diagonal is A[n,n] = n!n = n.

Similar to A114423 (with rows and columns exchanged). - Georg Fischer, Nov 02 2021

			Table begins:
  k / A(k,n)
  1 | 1 2 6 24 120 720 5040 40320 362880 3628800 ... = A000142.
  2 | 1 2 3  8  15  48  105   384    945    3840 ... = A006882.
  3 | 1 2 3  4  10  18   28    80    162     280 ... = A007661.
  4 | 1 2 3  4   5  12   21    32     45     120 ... = A007662.
  5 | 1 2 3  4   5   6   14    24     36      50 ... = A085157.
  6 | 1 2 3  4   5   6    7    16     27      40 ... = A085158.

Alois P. Heinz, Antidiagonals n = 1..141, flattened
Eric Weisstein's World of Mathematics, Multifactorial.

Cf. A000142 (n!), A006882 (n!!), A007661 (n!!!), A007662(n!4), A085157 (n!5), A085158 (n!6), A114799 (n!7), A114800 (n!8), A114806 (n!9), A288327 (n!10).

Cf. A114423 (transposed).

A:= proc(k,n) option remember; if n >= 1 then n* A(k, n-k) elif n >= 1-k then 1 else 0 fi end: seq(seq(A(1+d-n, n), n=1..d), d=1..16); # Alois P. Heinz, Feb 02 2009

A[k_, n_] := A[k, n] = If[n >= 1, n*A[k, n-k], If[n >= 1-k, 1, 0]]; Table[ A[1+d-n, n], {d, 1, 16}, {n, 1, d}] // Flatten (* Jean-François Alcover, May 27 2016, after Alois P. Heinz *)

A(k,n) = n!k.

A(k,n) = M(n,k) in A114423. - Georg Fischer, Nov 02 2021

Corrected and extended by Alois P. Heinz, Feb 02 2009

A142589 Square array T(n,m) = Product_{i=0..m} (1+n*i) read by antidiagonals.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 6, 3, 1, 1, 24, 15, 4, 1, 1, 120, 105, 28, 5, 1, 1, 720, 945, 280, 45, 6, 1, 1, 5040, 10395, 3640, 585, 66, 7, 1, 1, 40320, 135135, 58240, 9945, 1056, 91, 8, 1, 1, 362880, 2027025, 1106560, 208845, 22176, 1729, 120, 9, 1, 1, 3628800, 34459425, 24344320, 5221125, 576576, 43225, 2640, 153, 10, 1

Offset: 0

Roger L. Bagula and Gary W. Adamson, Sep 22 2008

Antidiagonal sums are {1, 2, 4, 11, 45, 260, 1998, 19735, 244797, 3729346, 68276276, ...}.

			The transpose of the array is:
    1,    1,     1,     1,      1,      1,      1,      1,     1,
    1,    2,     3,     4,      5,      6,      7,      8,     9,
    1,    6,    15,    28,     45,     66,     91,     120,   153, ... A000384
    1,   24,   105,   280,    585,   1056,   1729,    2640,  3825, ... A011199
    1,  120,   945,  3640,   9945,  22176,  43225,   76560, 126225,... A011245
    1,  720, 10395, 58240, 208845, 576576, 1339975, 2756160,...
        /      |       \       \
   A000142  A001147  A007559  A007696

G. C. Greubel, Antidiagonal rows n = 0..100, flattened

Cf. A000142, A006882(2n-1) = A001147, A007661(3n-2) = A007559, A007662(4n-3) = A007696, A153274.

function T(n,k)
  if k eq 0 or n eq 0 then return 1;
  else return (&*[j*k+1: j in [0..n]]);
  end if; return T; end function;
[T(n-k,k): k in [0..n], n in [0..12]]; // G. C. Greubel, Mar 05 2020

T:= (n, k)-> `if`(n=0, 1, mul(j*k+1, j=0..n)):
seq(seq(T(n-k, k), k=0..n), n=0..12); # G. C. Greubel, Mar 05 2020

T[n_, k_]= If[n==0, 1, Product[1 + k*i, {i,0,n}]]; Table[T[n-k, k], {n,0,10}, {k,0,n}]//Flatten

T(n, k) = if(n==0, 1, prod(j=0, n, j*k+1) );
for(n=0, 12, for(k=0, n, print1(T(n-k, k), ", "))) \\ G. C. Greubel, Mar 05 2020

def T(n, k):
    if (k==0 and n==0): return 1
    else: return product(j*k+1 for j in (0..n))
[[T(n-k, k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Mar 05 2020

Edited by M. F. Hasler, Oct 28 2014

More terms added by G. C. Greubel, Mar 05 2020

A214916 a(0) = a(1) = 1, a(n) = n! / a(n-2).

Original entry on oeis.org

1, 1, 2, 6, 12, 20, 60, 252, 672, 1440, 5400, 27720, 88704, 224640, 982800, 5821200, 21288960, 61102080, 300736800, 1990850400, 8089804800, 25662873600, 138940401600, 1007370302400, 4465572249600, 15397724160000, 90311261040000, 707173952284800, 3375972620697600

Offset: 0

Alex Ratushnyak, Aug 03 2012

nonn

a(n) is least k > a(n-1) such that k*a(n-2) is a factorial.

Two periodic subsets of these numbers appear in the coefficients of a series involved in a solution of a Riccati-type differential equation addressed by the Bernoulli brothers: z = 1 - x^4/12 + x^8/672 - x^12/88704 + ... = 1 - 2 * x^4/4! + 60 * x^8/8! - 5400 * x^12/12! + ... . See the MathOverflow question. - Tom Copeland, Jan 24 2017

Joerg Arndt, Table of n, a(n) for n = 0..100
MathOverflow, Link of a power series by the Bernoulli brothers for a Riccati equation to zonotopes?, a MathOverflow question by Tom Copeland, 2017.

Cf. A214914, A214915, A214961, A214963, A007662.

[1] cat  [n le 2 select n  else  Factorial(n)  div  Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jan 25 2017

import math
prpr = prev = 1
for n in range(2, 33):
    print(prpr, end=', ')
    cur = math.factorial(n) // prpr
    prpr = prev
    prev = cur

a(0) = a(1) = 1, for n>=2, a(n) = n! / a(n-2).

a(n) = n!!!! * (n-1)!!!! = A007662(n) * A007662(n-1), for n >= 1. - David Radcliffe, Jun 05 2025

A235136 a(n) = (2n - 1) a(n-2) for n>1, a(0) = a(1) = 1.

Original entry on oeis.org

1, 1, 3, 5, 21, 45, 231, 585, 3465, 9945, 65835, 208845, 1514205, 5221125, 40883535, 151412625, 1267389585, 4996616625, 44358635475, 184874815125, 1729986783525, 7579867420125, 74389431691575, 341094033905625, 3496303289504025, 16713607661375625

Offset: 0

Michael Somos, Jan 03 2014

			G.f. = 1 + x + 3*x^2 + 5*x^3 + 21*x^4 + 45*x^5 + 231*x^6 + 585*x^7 + ...

G. C. Greubel, Table of n, a(n) for n = 0..730

Cf. A007662, A007696, A008545, A196265.

Cf. A068465, A068466.

a[ n_] := 2^n If[ OddQ[n], 2 Pochhammer[ 1/4, (n + 1)/2], Pochhammer[ 3/4, n/2]]; (* Michael Somos, Jan 16 2014 *)
a[ n_] := If[ n < 0, 0, n! SeriesCoefficient[ (-2 Gamma[5/2] HermiteH[ -3/2, x] + (3 Gamma[5/4] + 2 Gamma[7/4]) Hypergeometric1F1[ 3/4, 1/2, x^2]) / (3 Gamma[5/4]), {x, 0, n}] // FullSimplify]; (* Michael Somos, Jan 16 2014 *)
RecurrenceTable[{a[0]==a[1]==1, a[n]==(2 n - 1) a[n - 2]}, a, {n, 25}] (* Vincenzo Librandi, Aug 08 2018 *)

{a(n) = if( n<0, (-1)^(-n\2) / a(-1-n), if( n<2, 1, (2*n - 1) * a(n-2)))};

Let b(n) = a(2*n - 2) / a(2*n + 1). Then b(-n) = b(n), 0 = b(n+1) * (b(n+1) + 2*b(n+2)) + b(n) * (2*b(n+1) - 5*b(n+2)) for all n in Z.
a(n-1) + a(n-2) = A196265(n) if n>1.
a(2*n) = A008545(n). a(2*n - 1) = A007696(n). a(n) = A007662(2*n - 1).
E.g.f. A(x) =: y satisfies 0 = y * 3 + y' * 2*x - y''.
0 = a(n)*(2*a(n+1) - a(n+3)) + a(n+1)*(a(n+2)) for all n in Z. - Michael Somos, Jan 24 2014
Let b(n) = a(n - 2) / a(n + 1). Then b(-n) = (-1)^n * b(n), 0 = b(n) * (b(n+1) - 4*b(n+3)) + b(n+2) * (2*b(n+1) + b(n+3)) for all n in Z. - Michael Somos, Sep 13 2014
a(n) ~ c * sqrt(Pi) * (2*n)^(n/2+1/4) / exp(n/2), where c = 2/Gamma(1/4) if n is odd, and 1/Gamma(3/4) if n is even. - Amiram Eldar, Sep 01 2025

A297707 a(n) = Product_{k=1..n-1} n!k, where n!k is k-tuple factorial of n.

Original entry on oeis.org

1, 2, 18, 768, 90000, 44789760, 30494620800, 121762322841600, 393644011735296000, 5618427494400000000000, 107587910030480590233600000, 5951222311476064581656248320000, 176804782652901880753915871232000000, 69819090744423637487544223697731584000000

Offset: 1

Lechoslaw Ratajczak, Jan 03 2018

nonn

What is the least n > 2 for which a(n) - prevprime(a(n)) is a composite number? If such a number n exists, it is greater than 250.

The least n for which nextprime(a(n)) - a(n) is a composite number is 158.

			a(2) = (2!1) = (2*1) = 2;
a(3) = (3!1)*(3!2) = (3*2*1)*(3*1) = 18;
a(4) = (4!1)*(4!2)*(4!3) = (4*3*2*1)*(4*2)*(4*1) = 768;
a(5) = (5!1)*(5!2)*(5!3)*(5!4) = (5*4*3*2*1)*(5*3*1)*(5*2)*(5*1) = 90000.

Michel Marcus, Table of n, a(n) for n = 1..100

Cf. A000142, A006882, A007661, A007662, A085157, A085158, A114799, A114800.

Cf. A114806, A288327, A006990, A033933.

b:= proc(n, k) option remember; `if`(n<1, 1, n*b(n-k, k)) end:
a:= n-> mul(b(n, k), k=1..n-1):
seq(a(n), n=1..20);  # Alois P. Heinz, Dec 02 2018

Array[(#^(# - 1)) Product[k^DivisorSigma[0, # - k], {k, # - 1}] &, 13] (* Michael De Vlieger, Jan 04 2018 *)

a(n) = (n^(n-1))*prod(k=1, n-1, k^numdiv(n-k)); \\ Michel Marcus, Dec 02 2018

a(n) = Product_{t=1..n-1} (Product_{k=0..floor((n-1)/t)} (n-t*k)).

a(n) = (n^(n-1))*Product_{k=1..n-1} k^tau(n-k).

cp's OEIS Frontend

A114799 Septuple factorial, 7-factorial, n!7, n!!!!!!!, a(n) = n*a(n-7) if n > 1, else 1.

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A114806 Nonuple factorial, 9-factorial, n!9, n!!!!!!!!!.

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A085146 Numbers k such that k!!!! + 1 is prime.

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A288091 Decimal expansion of m(4) = Sum_{n>=0} 1/n!!!!, the 4th reciprocal multifactorial constant.

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A288327 Decuple factorial, 10-factorial, n!10, n!!!!!!!!!!.

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A129116 Multifactorial array: A(k,n) = k-tuple factorial of n, for positive n, read by ascending antidiagonals.

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A235136 a(n) = (2n - 1) a(n-2) for n>1, a(0) = a(1) = 1.