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A075374
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a(n+2) = n*a(n+1) - a(n), with a(1)=1, a(2)=2.
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5
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1, 2, 1, 0, -1, -4, -19, -110, -751, -5898, -52331, -517412, -5639201, -67153000, -867349799, -12075744186, -180268812991, -2872225263670, -48647560669399, -872783866785512, -16534245908255329, -329812134298321068, -6909520574356487099, -151679640501544395110
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Starting with offset 5 unsigned: (1, 4, 19, 110, 751, ...) = eigensequence of triangle A003991. - Gary W. Adamson, May 17 2010
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LINKS
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FORMULA
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a(n+1) = (a(n) + a(n+2))/n with a(1) = 1, a(2) = 2.
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MAPLE
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a[1] := 1:a[2] := 2:for n from 1 to 45 do a[n+2] := n*a[n+1]-a[n]:od:seq(a[i], i=1..45);
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MATHEMATICA
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a[n_]:= a[n]= If[n<3, n, (n-2)*a[n-1] -a[n-2]];
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PROG
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(Magma) [n le 2 select n else (n-2)*Self(n-1) - Self(n-2): n in [1..50]]; // G. C. Greubel, Mar 04 2022
(Sage)
@CachedFunction
def a(n): return n if (n<3) else (n-2)*a(n-1) - a(n-2) # A075374
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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