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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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10
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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,...].
Stirling transform of a(n-1) = [0,1,0,6,0,120,0,...] is A000670(n-1) = [0,1,3,13,75,...].
Stirling transform of a(n-1) = [1,1,0,6,0,120,0,...] is A052856(n-1) = [1,2,4,14,76,...]. (End)
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REFERENCES
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D. R. Hofstadter, 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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FORMULA
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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, Apr 22 2007
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MATHEMATICA
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nn = 20; Rest[ Range[0, nn]! CoefficientList[ Series[ Log[(1 - x^2)^(-1/2)], {x, 0, nn}], x]] (* Geoffrey Critzer, May 29 2013 *)
Riffle[Range[1, 25, 2]!, 0, {1, -1, 2}] (* Harvey P. Dale, Mar 10 2017 *)
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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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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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