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A005212
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n! if n is odd otherwise 0 (from the Taylor series for sin x).
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3
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0, 1, 0, 6, 0, 120, 0, 5040, 0, 362880, 0, 39916800, 0, 6227020800, 0, 1307674368000, 0, 355687428096000, 0, 121645100408832000, 0, 51090942171709440000, 0, 25852016738884976640000, 0
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OFFSET
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0,4
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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)=[1,0,6,0,120,0,5040,...] is A089677(n)=[1,1,7,37,271,...]. - Michael Somos Mar 04 2004
Stirling transform of a(n-1)=[0,1,0,6,0,120,0,...] is A00670(n-1)=[0,1,3,13,75,...]. - Michael Somos Mar 04 2004
Stirling transform of a(n-1)=[1,1,0,6,0,120,0,...] is A052856(n-1)=[1,2,4,14,76,...]. - Michael Somos Mar 04 2004
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REFERENCES
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Hofstadter, D. R., Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought, (together with the Fluid Analogies Research Group), NY: Basic Books, 1995.
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LINKS
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Table of n, a(n) for n=0..24.
Index entries for sequences related to factorial numbers
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FORMULA
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E.g.f. -log(cos(arcsin(x))). [From Vladimir Kruchinin, Jun 15 2011]
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MAPLE
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BB:=[T, {T=Prod(Z, F), F=Sequence(B), B=Prod(Z, Z)}, labeled]: seq(count(BB, size=i), i=0..24); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2007
a:=n->n!-sum((-1)^k*n!, k=0..n): seq(a(n), n=0..24); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 25 2008
a:=n->n!-(-1)^n*n!: seq(a(n)/2, n=0..24); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 25 2008
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PROG
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(PARI) a(n)=if(n<0, 0, if(n%2, n!, 0))
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CROSSREFS
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Sequence in context: A085511 A187525 A187696 * A167028 A052679 A134680
Adjacent sequences: A005209 A005210 A005211 * A005213 A005214 A005215
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KEYWORD
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nonn
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AUTHOR
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Russ Cox
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STATUS
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approved
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