A203156 (n-1)-st elementary symmetric function of {4,9,16,25,..., (n+1)^2}.

1, 13, 244, 6676, 254736, 13000464, 857431296, 71077637376, 7239445632000, 889141110912000, 129629670893568000, 22136856913815552000, 4377599743151480832000, 992559996665635184640000, 255805371399126806691840000

Offset: 1

Author

Clark Kimberling, Dec 29 2011

Keywords

• nonn

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..251

Crossrefs

Cf. A066989.

Programs

Maple

f:= proc(n) local i,x; coeff(mul(x+i^2,i=2..n+1),x,1) end proc:
map(f, [$1..26]); # Robert Israel, Dec 16 2024

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 *)

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