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A217260
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Expansion of e.g.f. 2*arctan(1+x) - Pi/2.
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4
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1, -1, 1, 0, -6, 30, -90, 0, 2520, -22680, 113400, 0, -7484400, 97297200, -681080400, 0, 81729648000, -1389404016000, 12504636144000, 0, -2375880867360000, 49893498214560000, -548828480360160000
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OFFSET
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1,5
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LINKS
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FORMULA
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E.g.f.: 2*arctan(1+x) - Pi/2.
a(n) = n!*(Sum_{i=1..floor(n+1)/2} ((-1)^(n+i)*binomial(n-1, 2*i-2))/(2*i-1))/2^(n-1).
E.g.f. is the series reversion of sec(x) + tan(x) - 1.
a(n) = (n-1)*a(n-1) - (n-1)*(n-2)*a(n-2)/2.
a(n) = 2^(1-n/2)*(n-1)!*sin(3*Pi*n/4). (End)
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MAPLE
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seq(2^(1-n/2)*sin(3/4*Pi*n)*(n-1)!, n=1..50); # Robert Israel, Jan 17 2017
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MATHEMATICA
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Table[2^(1 - n/2)*(n - 1)!*Sin[3*Pi*n/4], {n, 30}] (* Wesley Ivan Hurt, Oct 14 2023 *)
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PROG
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(Maxima)
a(n):=n!*sum(((-1)^(n+i)*binomial(n-1, 2*i-2))/(2*i-1), i, 1, (n+1)/2)/2^(n-1);
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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