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A005359
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a(n) = n! if n is even, otherwise 0 (from Taylor series for cos x).
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10
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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
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OFFSET
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0,3
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COMMENTS
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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.
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REFERENCES
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Douglas Hofstadter, "Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought".
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for sequences related to factorial numbers
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FORMULA
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E.g.f. 1/(1-x^2) = d/dx log(sqrt((1+x)/(1-x))). a(2n)=(2n)!, a(2n+1)=0.
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MAPLE
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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
a:=n->n!+(-1)^n*n!: seq(a(n)/2, n=0..25); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 25 2008
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MATHEMATICA
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Riffle[Range[0, 30, 2]!, 0] (* From Harvey P. Dale, Nov 16 2011 *)
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PROG
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(PARI) a(n)=if(n<0, 0, if(n%2, 0, n!))
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CROSSREFS
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Contribution 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)
Sequence in context: A133490 A051728 A201954 * A008842 A130915 A127067
Adjacent sequences: A005356 A005357 A005358 * A005360 A005361 A005362
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Russ Cox
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STATUS
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approved
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