The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A110903 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A110903

Difference between the factorial of n and the double factorial of n.
(history; published version)

#13 by Michael De Vlieger at Thu May 09 13:26:35 EDT 2024

STATUS

proposed

approved

#12 by Michel Marcus at Thu May 09 13:02:10 EDT 2024

STATUS

editing

proposed

#11 by Michel Marcus at Thu May 09 13:02:06 EDT 2024

MATHEMATICA

Table[(n!-n!!), {n, 0, 15}] - _(* _Zerinvary Lajos_, Mar 21 2007 *)

STATUS

approved

editing

#10 by N. J. A. Sloane at Thu Jan 02 21:53:30 EST 2020

STATUS

reviewed

approved

#9 by Michel Marcus at Thu Jan 02 17:34:00 EST 2020

STATUS

proposed

reviewed

#8 by Andrew Howroyd at Thu Jan 02 17:31:33 EST 2020

STATUS

editing

proposed

#7 by Andrew Howroyd at Thu Jan 02 17:31:07 EST 2020

FORMULA

a(n) = A000142(n) - A006882(n). - Andrew Howroyd, Jan 02 2020

#6 by Andrew Howroyd at Thu Jan 02 17:30:35 EST 2020

DATA

0, 0, 0, 3, 16, 105, 672, 4935, 39936, 361935, 3624960, 39906405, 478955520, 6226885665, 87177646080, 1307672340975, 20922779566080, 355687393636575, 6402373519933440, 121645099754102925, 2432902004460748800, 51090942157960129425, 1124000727695858073600

LINKS

Andrew Howroyd, <a href="/A110903/b110903.txt">Table of n, a(n) for n = 0..200</a>

FORMULA

a(n) = n! - n!!.

a(n) = A000142(n) - A006882(n). - Andrew Howroyd, Jan 02 2020

EXAMPLE

a(7) = 7*6*5*4*3*2*1 - 7*5*3*1 = 4935.

PROG

(PARI) a(n)={n! - if(n%2, n!/((n\2)!*2^(n\2)), (n/2)!*2^(n/2))} \\ Andrew Howroyd, Jan 02 2020

CROSSREFS

Cf. A000142 (factorials), A006882 (double factorials).

EXTENSIONS

Terms a(15) and beyond from Andrew Howroyd, Jan 02 2020

STATUS

approved

editing

#5 by N. J. A. Sloane at Wed Oct 09 02:24:13 EDT 2013

MATHEMATICA

Table[(n!-n!!), {n, 0, 15}] - _Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), _, Mar 21 2007

Discussion

Wed Oct 09

02:24

OEIS Server: https://oeis.org/edit/global/1991

#4 by Russ Cox at Fri Mar 30 18:53:35 EDT 2012

AUTHOR

_Paolo P. Lava (paoloplava(AT)gmail.com), _, Sep 21 2005

Discussion

Fri Mar 30

18:53

OEIS Server: https://oeis.org/edit/global/262