login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A005359 a(n) = n! if n is even, otherwise 0 (from Taylor series for cos x). 20
1, 0, 2, 0, 24, 0, 720, 0, 40320, 0, 3628800, 0, 479001600, 0, 87178291200, 0, 20922789888000, 0, 6402373705728000, 0, 2432902008176640000, 0, 1124000727777607680000, 0, 620448401733239439360000, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Normally sequences like this are not included, since with the alternating 0's deleted it is already in the database.
Stirling transform of a(n)=[0,2,0,24,0,720,...] is A052841(n)=[0,2,6,38,270,...]. - Michael Somos, Mar 04 2004
Stirling transform of a(n-1)=[1,0,2,0,24,0,...] is A000670(n-1)=[1,1,3,13,75,...]. - Michael Somos, Mar 04 2004
Stirling transform of a(n-1)=[0,0,2,0,24,0,...] is A052875(n-1)=[0,0,2,12,74,...]. - Michael Somos, Mar 04 2004
Stirling transform of (-1)^n*A052811(n)=[0,2,-6,46,-340,...] is a(n)=[0,2,0,24,0,...]. - Michael Somos, Mar 04 2004
Also n-th derivative of arctanh(x) at x=0. - Michel Lagneau, Aug 13 2012
Binomial convolution square of A177145 (with offset 0) because each permutation in S_{2n} uniquely determines a bi-partition of its elements into even and odd cycles and these are both enumerated by A177145. - Michael Somos, Mar 19 2019
REFERENCES
Douglas Hofstadter, "Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought".
LINKS
Michael Somos, Number of permutations with all cycles of even length, answer to Mathematics Stack Exchange question 3152701, Mar 18 2019.
FORMULA
E.g.f. 1/(1-x^2) = d/dx log(sqrt((1+x)/(1-x))). a(2n)=(2n)!, a(2n+1)=0. - Michael Somos, Mar 04 2004
a(n) = Product_{k=0..n/2-1} binomial(n-2k,2)*2^(n/2) for even n. - Geoffrey Critzer, Jun 05 2016
From Ilya Gutkovskiy, Jun 05 2016: (Start)
D-finite with recurrence a(n) = n*(n - 1)*a(n-2), a(0)=1, a(1)=0.
a(n) = n!*((-1)^n + 1)/2. (End)
MAPLE
BB:={E=Prod(Z, Z), S=Union(Epsilon, Prod(S, E))}: ZL:=[S, BB, labeled]: > seq(count(ZL, size=n), n=0..25); # Zerinvary Lajos, Apr 22 2007
a:=n->n!+(-1)^n*n!: seq(a(n)/2, n=0..25); # Zerinvary Lajos, Mar 25 2008
MATHEMATICA
Riffle[Range[0, 30, 2]!, 0] (* Harvey P. Dale, Nov 16 2011 *)
a[ n_] := If[n >= 0 && EvenQ[n], n!, 0]; (* Michael Somos, Mar 19 2019 *)
PROG
(PARI) {a(n) = if(n<0, 0, if(n%2, 0, n!))}; /* Michael Somos, Mar 04 2004 */
CROSSREFS
From Johannes W. Meijer, Nov 12 2009: (Start)
Equals the first right hand column of A167565.
Equals the first left hand column of A167568.
(End)
Cf. A177145.
Bisection (even part) gives A010050.
Sequence in context: A133490 A051728 A201954 * A008842 A347898 A130915
KEYWORD
nonn
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)