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A024419
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a(n) = n! (1/C(n,0) + 1/C(n,1) + ... + 1/C(n,[ n/2 ])).
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3
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1, 1, 3, 8, 34, 156, 924, 6144, 48096, 420480, 4134240, 44720640, 530444160, 6824805120, 94787884800, 1412038656000, 22464536371200, 380017225728000, 6811416338227200, 128936055177216000, 2570286167543808000, 53818546503794688000, 1180914445357903872000
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OFFSET
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0,3
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COMMENTS
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Half-convolution of factorials (A000142) with itself. For the definition of the half-convolution of a sequence with itself see a comment to A201204. - Vladimir Reshetnikov, Oct 05 2016
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LINKS
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FORMULA
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G.f.: (G(x)^2+H(x))/2 where G(x) = Sum_{k>=0} k!*x^k and H(x) = Sum_{k>=0} k!^2*x^(2*k). - Vladeta Jovovic, Sep 22 2007
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EXAMPLE
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a(3)=3!*(1/1 + 1/3)=6*4/3=8.
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MAPLE
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a:=proc(n) options operator, arrow: factorial(n)*(sum(1/binomial(n, k), k= 0.. floor((1/2)*n))) end proc: seq(a(n), n=0..21); # Emeric Deutsch, Oct 11 2007
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MATHEMATICA
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PROG
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(PARI) a(n) = sum(k=0, n\2, k!*(n-k)!); \\ Michel Marcus, Oct 05 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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