A000722 -id:A000722 - cp's OEIS frontend

A079288 a(n) = (3^n)!.

1, 6, 362880, 10888869450418352160768000000

Offset: 0

Cino Hilliard, Feb 08 2003

Next term is too large to include.

Sum_{n>0} 1/a(n) = 0.1666694223985890... or about 1/6. This is evident since 1/3! =0.166666666666.. 1/9! =0.0000027557319223985.. 1/27!=0.00000000000000000000000000091836898637955461.. for example shows that succeeding terms have little influence on the first term 1/6. A000722 has the same property of about 1/2 but it is not evident since in 1/2! + 1/4! + 1/8! 1/4! and 1/8! have an immediate effect on the first term 1/2. So the limit of sum(1/(x^n)!) -> 1/x! as x,n -> oo

Cf. A000142, A000244.

atonfact(a,n) = {sr=0; for(x=1,n, y =(a^x)!; \-((a-1)^x)!; sr+=1.0/y; print1(y" "); ); print(); print(sr) } usage: ? atonfact(3,n) n=1,2,..

a(n) = (3^n)! \\ Michel Marcus, Sep 14 2015

a(n) = A000142(A000244(n)). - Michel Marcus, Sep 14 2015

A244060 Sum of digits of (2^n)!.

Original entry on oeis.org

1, 2, 6, 9, 63, 108, 324, 828, 1989, 4635, 10845, 24363, 54279, 118827, 258705, 565389, 1216134, 2611359, 5584518, 11875977, 25184205, 53209728, 112069377, 235502361, 493827687, 1033041267, 2156974227, 4495662081, 9355185828, 19437382512, 40329016200

Offset: 0

Robert G. Wilson v, Jun 18 2014

			If n=4, 2^4! = 16! = 20922789888000, with digit sum 63. - _N. J. A. Sloane_, Jun 18 2014

Cf. A000722, A007953.

Cf. A116988, A244061.

f[n_] := Total[ IntegerDigits[ (2^n)!]]; Array[f, 20, 0]

a(n) = sumdigits((2^n)!); \\ Michel Marcus, Oct 25 2021

from math import factorial
def A244060(n): return sum(int(d) for d in str(factorial(2**n))) # Chai Wah Wu, Oct 26 2021

a(n) = A007953(A000722(n)). - Michel Marcus, Jun 19 2014

a(26)-a(30) from Chai Wah Wu, Oct 25 2021

A244061 The number of digits of (2^n)!.

Original entry on oeis.org

1, 1, 2, 5, 14, 36, 90, 216, 507, 1167, 2640, 5895, 13020, 28504, 61937, 133734, 287194, 613842, 1306594, 2771010, 5857670, 12346641, 25955890, 54436999, 113924438, 237949763, 496101303, 1032606162, 2146019444, 4453653132, 9230534755

Offset: 0

Robert G. Wilson v, Jun 18 2014

Cf. A000722, A061010, A244060.

LogBase10Stirling[n_] := Floor[ Log[10, 2 Pi n]/2 + n*Log[10, n/E] + Log[10, 1 + 1/(12 n) + 1/(288 n^2) - 139/(51840 n^3) - 571/(2488320 n^4) + 163879/(209018880 n^5)]]; Table[ LogBase10Stirling[2^n] + 1, {n, 0, 30}]
IntegerLength[(2^Range[0,30])!] (* Harvey P. Dale, Nov 05 2021 *)

A259326 Ceiling of ((2^n)!+(2^n-1)^2(2^(n-1))!2^(2^(n-1)))/(4^n*(n!)^2).

Original entry on oeis.org

1, 2, 26, 141907500, 17844701940490373256193966080, 59757436204078657410908164193971177467473348779378572774972093904092502425600000

Offset: 1

N. J. A. Sloane, Jun 24 2015

nonn

C. S. Lorens, Invertible Boolean functions, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541.
C. S. Lorens, Invertible Boolean functions, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541. [Annotated scan of page 530 only]

Cf. A259327, A259328, A259329, A259330, A259331.

# Maple code for A259326, A259327, A259328, A259329, A259330, A259331:
f:=n->((2^n)!+(2^n-1)^2*(2^(n-1))!*2^(2^(n-1)))/(4^n*(n!)^2);
f:=n->((2^n)!)/(4^n*(n!)^2);
f:=n->((2^n)!)/(2^(n*(n-1))*mul((2^i-1)^2,i=1..n));
f:=n->((2^n)!)/(4^(n^2));
f:=n->((2^n)!)/(2^(n*(n+1))*mul((2^i-1)^2,i=1..n));
f:=n->((2^n)!)/(4^n*2^(2*n^2));
[seq(ceil(f(n)),n=1..6)];

A259327 Ceiling of ((2^n)!)/(4^n*(n!)^2).

Original entry on oeis.org

1, 1, 18, 141891750, 17844701940490283892633600000, 59757436204078657410908164193971177467471236322918735173920946651136000000000000

Offset: 1

N. J. A. Sloane, Jun 24 2015

nonn

C. S. Lorens, Invertible Boolean functions, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541.
C. S. Lorens, Invertible Boolean functions, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541. [Annotated scan of page 530 only]

A259328 Ceiling of ((2^n)!)/(2^(n(n-1))Product((2^i-1)^2,i=1..n)).

Original entry on oeis.org

2, 1, 2, 51480, 2631645209144487019355, 312242081385925594286511113381220856098317029402428309504000000000000

Offset: 1

N. J. A. Sloane, Jun 24 2015

nonn

C. S. Lorens, Invertible Boolean functions, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541.
C. S. Lorens, Invertible Boolean functions, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541. [Annotated scan of page 530 only]

A259329 Ceiling of ((2^n)!)/(4^(n^2)).

Original entry on oeis.org

1, 1, 1, 4872, 233707130922139265799, 26869353034366501299843095760875674032159666449783949888006055355073

Offset: 1

N. J. A. Sloane, Jun 24 2015

nonn

C. S. Lorens, Invertible Boolean functions, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541.
C. S. Lorens, Invertible Boolean functions, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541. [Annotated scan of page 530 only]

A259330 Ceiling of ((2^n)!)/(2^(n(n+1))Product((2^i-1)^2,i=1..n)).

Original entry on oeis.org

1, 1, 1, 202, 2569966024555163105, 76230976900860740792605252290337123070878181006452224000000000000

Offset: 1

N. J. A. Sloane, Jun 24 2015

nonn

C. S. Lorens, Invertible Boolean functions, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541.
C. S. Lorens, Invertible Boolean functions, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541. [Annotated scan of page 530 only]

A079286 a(n) = (3^n)! - (2^n)!.

Original entry on oeis.org

0, 4, 362856, 10888869450418352160767959680

Offset: 0

Cino Hilliard, Feb 08 2003

Sum_{n>0} 1/a(n) = 0.25000275591...
The next term is too large to include.
The next term (a(4)) has 121 digits. - Harvey P. Dale, Jan 10 2024

Amiram Eldar, Table of n, a(n) for n = 0..5

Cf. A000722, A079288.

Table[(3^n)!-(2^n)!,{n,0,4}] (* Harvey P. Dale, Jan 10 2024 *)

atonfact(n) = {for(x=0, n, y = (3^x)!-(2^x)!; print1(y, ", "));}

a(n) = A079288(n) - A000722(n). - Michel Marcus, Jul 08 2024

A259331 Ceiling of ((2^n)!)/(4^n2^(2n^2)).

Original entry on oeis.org

1, 1, 1, 20, 228229620041151627, 6559900643155884106407005800995037605507731066841784640626478359

Offset: 1

N. J. A. Sloane, Jun 24 2015

nonn

C. S. Lorens, Invertible Boolean functions, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541.
C. S. Lorens, Invertible Boolean functions, IEEE Trans. Electron. Computers, EC-13 (1964), 529-541. [Annotated scan of page 530 only]

Cf. A259326, A259327, A259328, A259329, A259330.

f:=n->((2^n)!)/(4^n*2^(2*n^2));
[seq(ceil(f(n)),n=1..6)];

cp's OEIS Frontend

A079288 a(n) = (3^n)!.

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A244060 Sum of digits of (2^n)!.

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A244061 The number of digits of (2^n)!.

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A259326 Ceiling of ((2^n)!+(2^n-1)^2*(2^(n-1))!*2^(2^(n-1)))/(4^n*(n!)^2).

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A259327 Ceiling of ((2^n)!)/(4^n*(n!)^2).

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A259328 Ceiling of ((2^n)!)/(2^(n*(n-1))*Product((2^i-1)^2,i=1..n)).

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A259329 Ceiling of ((2^n)!)/(4^(n^2)).

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A259330 Ceiling of ((2^n)!)/(2^(n*(n+1))*Product((2^i-1)^2,i=1..n)).

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A079286 a(n) = (3^n)! - (2^n)!.

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Mathematica

PARI

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A259331 Ceiling of ((2^n)!)/(4^n*2^(2*n^2)).

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Maple

A259326 Ceiling of ((2^n)!+(2^n-1)^2(2^(n-1))!2^(2^(n-1)))/(4^n*(n!)^2).

A259328 Ceiling of ((2^n)!)/(2^(n(n-1))Product((2^i-1)^2,i=1..n)).

A259330 Ceiling of ((2^n)!)/(2^(n(n+1))Product((2^i-1)^2,i=1..n)).

A259331 Ceiling of ((2^n)!)/(4^n2^(2n^2)).