login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A203156 (n-1)-st elementary symmetric function of {4,9,16,25,..., (n+1)^2}. 1
1, 13, 244, 6676, 254736, 13000464, 857431296, 71077637376, 7239445632000, 889141110912000, 129629670893568000, 22136856913815552000, 4377599743151480832000, 992559996665635184640000, 255805371399126806691840000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
a(n) = gamma(2 + n)^2*(Pi^2/6 - 1 - digamma^(1)(2 + n)), where gamma(x) is the gamma function and digamma^(n)(x) is the n-th derivative of the digamma function. - Markus Bindhammer, Nov 26 2017
EXAMPLE
Let esf abbreviate "elementary symmetric function". Then
0th esf of {4}: 1;
1st esf of {4,9}: 4 + 9 = 13;
2nd esf of {4,9,16}: 4*9 + 4*16 + 9*16 = 244.
MATHEMATICA
f[k_] := (k + 1)^2; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 22}] (* A203156 *)
CROSSREFS
Cf. A066989.
Sequence in context: A218229 A020520 A259420 * A049665 A196665 A027400
KEYWORD
nonn
AUTHOR
Clark Kimberling, Dec 29 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)