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A190901
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a(n) = Product_{k in M_n} k; M_n = {k | 1 <= k <= 2n and k mod 2 = n mod 2}.
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2
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1, 1, 8, 15, 384, 945, 46080, 135135, 10321920, 34459425, 3715891200, 13749310575, 1961990553600, 7905853580625, 1428329123020800, 6190283353629375, 1371195958099968000, 6332659870762850625, 1678343852714360832000
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OFFSET
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0,3
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LINKS
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FORMULA
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a(2*k) = A006882(4*k) = 4^k * Gamma(2*k+1).
a(2*k+1) = A001147(2*k+1) = 4^k * Gamma(2*k+3/2) / sqrt(Pi/4).
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MAPLE
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A190901 := proc(n) local k; mul(k, k = select(k-> k mod 2 = n mod 2, [$1 .. 2*n])) end: seq(A190901(n), n=0..18);
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MATHEMATICA
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a[n_] := With[{m = Mod[n, 2]}, Product[If[Mod[k, 2] == m, k, 1], {k, 1, 2*n}]]; Table[a[n], {n, 0, 18}] (* Jean-François Alcover, Jan 27 2014 *)
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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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