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 A005359 a(n) = n! if n is even, otherwise 0 (from Taylor series for cos x). 10
 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. REFERENCES Douglas Hofstadter, "Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought". LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 FORMULA E.g.f. 1/(1-x^2) = d/dx log(sqrt((1+x)/(1-x))). a(2n)=(2n)!, a(2n+1)=0. 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 (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 MATHEMATICA Riffle[Range[0, 30, 2]!, 0] (* From Harvey P. Dale, Nov 16 2011 *) PROG (PARI) a(n)=if(n<0, 0, if(n%2, 0, n!)) CROSSREFS 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 KEYWORD nonn AUTHOR STATUS approved

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