Search: id:A005359
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%I A005359
%S A005359 1,0,2,0,24,0,720,0,40320,0,3628800,0,479001600,0,87178291200,
%T A005359 0,20922789888000,0,6402373705728000,0,2432902008176640000,
%U A005359 0,1124000727777607680000,0,620448401733239439360000,0
%N A005359 n! if n is even otherwise 0 (from Taylor series for cos x).
%C A005359 Normally sequences like this are not included, since with the alternating 
               0's deleted it is already in the database.
%C A005359 Stirling transform of a(n)=[0,2,0,24,0,720,...] is A052841(n)=[0,2,6,
               38,270,...]. -Michael Somos Mar 04 2004
%C A005359 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
%C A005359 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
%C A005359 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
%D A005359 Douglas Hofstadter, "Fluid Concepts and Creative Analogies: Computer 
               Models of the Fundamental Mechanisms of Thought".
%H A005359 <a href="Sindx_Fa.html#factorial">Index entries for sequences related 
               to factorial numbers</a>
%F A005359 E.g.f. 1/(1-x^2) = d/dx log(sqrt((1+x)/(1-x))). a(2n)=(2n)!, a(2n+1)=0.
%p A005359 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 (zerinvarylajos(AT)yahoo.com), 
               Apr 22 2007
%p A005359 a:=n->n!+(-1)^n*n!: seq(a(n)/2, n=0..25); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Mar 25 2008
%o A005359 (PARI) a(n)=if(n<0,0,if(n%2,0,n!))
%Y A005359 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Nov 12 
               2009: (Start)
%Y A005359 Equals the first right hand column of A167565.
%Y A005359 Equals the first left hand column of A167568.
%Y A005359 (End)
%Y A005359 Sequence in context: A138551 A133490 A051728 this_sequence A008842 A130915 
               A127067
%Y A005359 Adjacent sequences: A005356 A005357 A005358 this_sequence A005360 A005361 
               A005362
%K A005359 nonn
%O A005359 0,3
%A A005359 N. J. A. Sloane (njas(AT)research.att.com), Russ Cox (rsc(AT)swtch.com)

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