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A285524
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a(n) is the value d<n/2 maximizing the expression d!*(d + 1)!*2^(n-2*d-1)*stirling2(n-d, d+1), for n>=4.
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2
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1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 24
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OFFSET
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4,4
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COMMENTS
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In case the maximum should turn out not to be unique, use the smallest value. - N. J. A. Sloane, Apr 22 2017
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LINKS
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MAPLE
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f:= n -> max[index]([seq(d!*(d+1)!*2^(n-2*d-1)*Stirling2(n-d, d+1), d=1..n/2)]):
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MATHEMATICA
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a[n_] := MaximalBy[Table[{d, d! (d+1)! 2^(n-2d-1) StirlingS2[n-d, d+1]}, {d, 1, n/2}], Last][[All, 1]] // Min;
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PROG
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(PARI) half(n) = if (n % 2, n\2, n/2 - 1);
a(n) = {v = vector(half(n), d, d!*(d + 1)!*(2^(n-2*d-1)*stirling(n-d, d+1, 2))); w = vecsort(v, , 1); w[#w]; }
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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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