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A130783
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Maximum value of the n-th difference of a permutation of 0..n.
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1
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0, 1, 3, 10, 25, 66, 154, 372, 837, 1930, 4246, 9516, 20618, 45332, 97140, 210664, 447661, 960858, 2028478, 4319100, 9070110, 19188796, 40122028, 84438360, 175913250, 368603716, 765561564, 1598231992, 3310623412, 6889682280
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n) = (n+1)*(2^(n-1)-binomial(n-1,n/2)) if n is even else ((n+1)/2)*(2^n-binomial(n,(n+1)/2)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 23 2007
a(n) = (n+1)*(2^n-binomial(n,[n/2]))/2, where [x] is floor. - Graeme McRae (g_m(AT)mcraefamily.com), Jan 30, 2012
G.f.: (1-sqrt((1-2*x)/(1+2*x)))/(2*(1-2*x)^2). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 24 2007
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EXAMPLE
| a(1)=1 because 0 1 has a first difference of 1; a(2)=3 because 2 0 1 has a second difference of 3.
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PROG
| (PARI) a(n)=(n+1)*(2^n-binomial(n, n\2))/2 \\ Charles R Greathouse IV, Jan 30 2012
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CROSSREFS
| Cf. A000346, A033504.
Sequence in context: A089117 A176610 A026965 * A026975 A026985 A027227
Adjacent sequences: A130780 A130781 A130782 * A130784 A130785 A130786
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KEYWORD
| nonn,easy
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AUTHOR
| R. H. Hardin (rhhardin(AT)att.net), Aug 19 2007
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