A203240 Real part of even numbered terms of the sequence s(n)=(n-1)-st elementary symmetric function of (i, 2i, 3i,...,ni).

1, -11, 274, -13068, 1026576, -120543840, 19802759040, -4339163001600, 1223405590579200, -431565146817638400, 186244810780170240000, -96538966652493066240000, 59190128811701203599360000, -42373564558110787183902720000

Offset

1,2

Links

Table of n, a(n) for n=1..14.

Formula

a(n) = (-1)^(n+1)*(2*n - 1)!*Sum(i=1..2*n-1, 1/i). - Arkadiusz Wesolowski, Mar 25 2013

From Anton Zakharov, Oct 26 2016: (Start)

a(n) = (-1)^(n+1)*Sum_{k=1..n} A094310(2n-1,k).

(-1)^(n+1)*a(n) = A000254(2*n-1) (signed bisection of A000254). (End)

Example

See A203239.

Maple

a := n -> (-1)^(n-1)*(2*n-1)!*harmonic(2*n-1):
seq(a(n), n = 1..14); # Peter Luschny, Oct 26 2016

Mathematica

f[k_] := k*I; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 22}]
Table[-I*a[2 n], {n, 1, 22}]     (* A203239 *)
Table[a[2 n - 1], {n, 1, 22}]    (* A203240 *)
Table[(-1)^(n + 1)*(2*n - 1)!*HarmonicNumber[2*n - 1], {n, 14}] (* Arkadiusz Wesolowski, Mar 25 2013 *)

Crossrefs

Cf. A203239, A094310, A000254.

Sequence in context: A168147 A108519 A160195 * A062210 A049080 A210807

Adjacent sequences: A203237 A203238 A203239 * A203241 A203242 A203243

Keyword

sign

Author

Clark Kimberling, Dec 30 2011

Status

approved