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

%I

%S 1,13,244,6676,254736,13000464,857431296,71077637376,7239445632000,

%T 889141110912000,129629670893568000,22136856913815552000,

%U 4377599743151480832000,992559996665635184640000,255805371399126806691840000

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

%F 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

%e Let esf abbreviate "elementary symmetric function". Then

%e 0th esf of {4}: 1;

%e 1st esf of {4,9}: 4 + 9 = 13;

%e 2nd esf of {4,9,16}: 4*9 + 4*16 + 9*16 = 244.

%t f[k_] := (k + 1)^2; t[n_] := Table[f[k], {k, 1, n}]

%t a[n_] := SymmetricPolynomial[n - 1, t[n]]

%t Table[a[n], {n, 1, 22}] (* A203156 *)

%Y Cf. A066989.

%K nonn

%O 1,2

%A _Clark Kimberling_, Dec 29 2011

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Last modified February 5 03:48 EST 2023. Contains 360082 sequences. (Running on oeis4.)