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%I #25 Oct 26 2016 16:16:50
%S 1,-11,274,-13068,1026576,-120543840,19802759040,-4339163001600,
%T 1223405590579200,-431565146817638400,186244810780170240000,
%U -96538966652493066240000,59190128811701203599360000,-42373564558110787183902720000
%N Real part of even numbered terms of the sequence s(n)=(n-1)-st elementary symmetric function of (i, 2i, 3i,...,ni).
%F a(n) = (-1)^(n+1)*(2*n - 1)!*Sum(i=1..2*n-1, 1/i). - _Arkadiusz Wesolowski_, Mar 25 2013
%F From _Anton Zakharov_, Oct 26 2016: (Start)
%F a(n) = (-1)^(n+1)*Sum_{k=1..n} A094310(2n-1,k).
%F (-1)^(n+1)*a(n) = A000254(2*n-1) (signed bisection of A000254). (End)
%e See A203239.
%p a := n -> (-1)^(n-1)*(2*n-1)!*harmonic(2*n-1):
%p seq(a(n), n = 1..14); # _Peter Luschny_, Oct 26 2016
%t f[k_] := k*I; t[n_] := Table[f[k], {k, 1, n}]
%t a[n_] := SymmetricPolynomial[n - 1, t[n]]
%t Table[a[n], {n, 1, 22}]
%t Table[-I*a[2 n], {n, 1, 22}] (* A203239 *)
%t Table[a[2 n - 1], {n, 1, 22}] (* A203240 *)
%t Table[(-1)^(n + 1)*(2*n - 1)!*HarmonicNumber[2*n - 1], {n, 14}] (* _Arkadiusz Wesolowski_, Mar 25 2013 *)
%Y Cf. A203239, A094310, A000254.
%K sign
%O 1,2
%A _Clark Kimberling_, Dec 30 2011
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