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

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 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 Adjacent sequences: A203153 A203154 A203155 * A203157 A203158 A203159 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.

Last modified November 30 04:37 EST 2022. Contains 358431 sequences. (Running on oeis4.)