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%I #13 Jul 14 2020 21:40:22
%S 1,17,1393,357904,224021776,290539581696,697854274212096,
%T 2859056348455305216,18760911610508623282176,
%U 187626456226399005573120000,2747212346823835568109649920000,56968733990900457398848318341120000
%N (n-1)-st elementary symmetric function of (1,16,...,n^4).
%F a(n) ~ 2 * Pi^6 * n^(4*n+2) / (45*exp(4*n)). - _Vaclav Kotesovec_, Aug 27 2017
%F Sum_{n>=1} a(n) * x^n / (n!)^4 = polylog(4,x) / (1 - x). - _Ilya Gutkovskiy_, Jul 14 2020
%t f[k_] := k^4; t[n_] := Table[f[k], {k, 1, n}]
%t a[n_] := SymmetricPolynomial[n - 1, t[n]]
%t Table[a[n], {n, 1, 14}] (* A203229 *)
%t Table[(n!)^4 * Sum[1/i^4, {i, 1, n}], {n, 1, 20}] (* _Vaclav Kotesovec_, Aug 27 2017 *)
%Y Cf. A000583, A203148.
%Y Column k=4 of A291556.
%K nonn
%O 1,2
%A _Clark Kimberling_, Dec 30 2011
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