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A033030
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Derangement numbers d(n,3) where d(n,k) = k(n-1)(d(n-1,k) + d(n-2,k)), with d(0,k) = 1 and d(1,k) = 0.
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5
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1, 0, 3, 18, 189, 2484, 40095, 766422, 16936857, 424878696, 11929019931, 370616958810, 12624017298453, 467806833261468, 18736803171836919, 806593620214132254, 37139869052368612785, 1821430208283971761872, 94787073944153359107507, 5216859224231615866946466
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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(n) = 3(n-1)(a(n-1)+a(n-2)), n>1. - Gary Detlefs, May 16 2010
a(n) ~ Gamma(2/3) * 3^(n + 1/2) * n^(n-1/6) / (sqrt(2*Pi) * exp(n + 1/3)). - Vaclav Kotesovec, Oct 31 2017
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EXAMPLE
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3= 3*(1+0), 18 =6*(0+3), 189=9*(18+3), 2484=12*(189+18)... [From Gary Detlefs, May 16 2010]
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MAPLE
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k := 3; d := proc(n) global k; option remember; if n = 0 then RETURN(1) end if; if n = 1 then RETURN(0) end if; k*(n - 1)*(d(n - 1) + d(n - 2)) end proc;
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MATHEMATICA
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d[n_, k_] := d[n, k] = k(n-1)(d[n-1, k] + d[n-2, k]);
d[0, _] = 1; d[1, _] = 0;
a[n_] := d[n, 3];
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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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STATUS
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approved
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