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A285740 Denominator of discriminant of n-th Bernoulli polynomial.

%I A285740 #12 Feb 16 2025 08:33:44
%S A285740 1,3,16,3375,559872,1815156,80621568,124556484375,80000000000000,
%T A285740 11881340006899968,1218719480020992,
%U A285740 3405780508865246682482292626953125,1526226812966134209666905971200000000000000000,18160335421875000000000000
%N A285740 Denominator of discriminant of n-th Bernoulli polynomial.
%H A285740 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BernoulliPolynomial.html">Bernoulli Polynomial</a>.
%H A285740 <a href="/index/Di#discriminants">Index entries for sequences related sequences related to discriminants of polynomials</a>.
%e A285740 1, 1/3, 1/16, 28/3375, 343/559872, 31/1815156, 29791/80621568, 178035712/124556484375, 11651995228221/80000000000000, ...
%e A285740 The first few Bernoulli polynomials are
%e A285740 0 | 1;
%e A285740 1 | x - 1/2;
%e A285740 2 | x^2 - x + 1/6;
%e A285740 3 | x^3 - 3*x^2/2 + x/2;
%e A285740 4 | x^4 - 2*x^3 + x^2 - 1/30;
%e A285740 5 | x^5 - 5*x^4/2 + 5*x^3/3 - x/6, etc.
%t A285740 Table[Denominator[Discriminant[BernoulliB[n, x], x]], {n, 1, 14}]
%o A285740 (PARI) a(n) = denominator(poldisc(bernpol(n))); \\ _Michel Marcus_, Mar 02 2023
%Y A285740 Cf. A053382, A053383, A196838, A196839, A285739 (numerators).
%K A285740 nonn,frac
%O A285740 1,2
%A A285740 _Ilya Gutkovskiy_, Apr 25 2017