login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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). 2
3, -50, 1764, -109584, 10628640, -1486442880, 283465647360, -70734282393600, 22376988058521600, -8752948036761600000, 4148476779335454720000, -2342787216398718566400000, 1554454559147562279567360000 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 21 05:51 EDT 2020. Contains 337267 sequences. (Running on oeis4.)