A203239 Odd numbered terms of the sequence whose n-th term is the (n-1)-st elementary symmetric function of (i, 2i, 3i, ..., ni), where i=sqrt(-1).

3, -50, 1764, -109584, 10628640, -1486442880, 283465647360, -70734282393600, 22376988058521600, -8752948036761600000, 4148476779335454720000, -2342787216398718566400000, 1554454559147562279567360000

Offset

1,1

Links

Table of n, a(n) for n=1..13.

Formula

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

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

Example

The first 10 terms of the "full sequence" are as follows:
1, 3i, -11, -50i, 274, 1764i, -13068, -109584i, 1026576, 10628640i;
Abbreviate "elementary symmetric function" as esf. Then, starting with {i, 2i, 3i, 4i, ...}:
0th esf of {i}: 1
1st esf of {i, 2i}: i+2i = 3i
2nd esf of {i, 2i, 3i}: -2-3-6 = -11.
For the alternating terms 3i, -50i, ..., see A203240.

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)!*HarmonicNumber[2*n], {n, 13}] (* Arkadiusz Wesolowski, Mar 25 2013 *)

Crossrefs

Cf. A000254, A094310, A165675, A203240.

Sequence in context: A326250 A308331 A245141 * A279970 A217767 A185157

Adjacent sequences: A203236 A203237 A203238 * A203240 A203241 A203242

Keyword

sign

Author

Clark Kimberling, Dec 30 2011

Status

approved