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A092396
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Row 2 of array in A288580.
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8
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1, -1, -4, 9, 64, -225, -2304, 11025, 147456, -893025, -14745600, 108056025, 2123366400, -18261468225, -416179814400, 4108830350625, 106542032486400, -1187451971330625, -34519618525593600, 428670161650355625, 13807847410237440000, -189043541287806830625, -6682998146554920960000
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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REFERENCES
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F. Smarandache, Back and Forth Factorials, Arizona State Univ., Special Collections, 1972.
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LINKS
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FORMULA
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a(n) = !n!_2 = Prod_{i=0, 1, 2, ... .}_{0<|n-2i|<=n}(n-2i) = n(n-2)(n-4)... = (-1)^(Int(n+1)/2) * (n!!)^2
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EXAMPLE
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!3!_2 = 3(3-2)(3-4)(3-6) = 9 and !4!_2 = 4(4-2)(4-6)(4-8) = 64.
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MAPLE
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T:=proc(n, k) local i, p;
p:=1;
for i from 0 to floor(2*n/k) do
if n-k*i <> 0 then p:=p*(n-k*i) fi; od:
p;
end;
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MATHEMATICA
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T[n_, k_] := Module[{i, p = 1}, For[i = 0, i <= Floor[2n/k], i++, If[n - k i != 0, p *= (n - k i)]]; p]; T[_, 0] = 1;
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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J. Dezert (Jean.Dezert(AT)onera.fr), Mar 21 2004
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EXTENSIONS
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STATUS
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approved
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