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A092398
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Row 4 of array in A288580.
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8
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1, 1, -4, -3, -16, -15, 144, 105, 1024, 945, -14400, -10395, -147456, -135135, 2822400, 2027025, 37748736, 34459425, -914457600, -654729075, -15099494400, -13749310575, 442597478400, 316234143225, 8697308774400, 7905853580625, -299195895398400, -213458046676875, -6818690079129600, -6190283353629375
(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!_4 = Prod_{i=0, 1, 2, ... .}_{0<|n-4i|<=n}(n-4i) = n*(n-4)*(n-8)....
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EXAMPLE
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!9!_4 = 9*(9-4)*(9-8)*(9-12)*(9-16) = 9*(5)*(1)*(-3)*(-7) = 945.
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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[2 n/k], i++,
If[n - k i != 0, p *= (n - k i)]]; p];
T[_, 0] = 1;
a[n_] := T[n, 4];
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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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