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A285739 Numerator of discriminant of n-th Bernoulli polynomial.

%I A285739 #13 Feb 16 2025 08:33:44
%S A285739 1,1,1,28,343,31,29791,178035712,11651995228221,1087618835548371875,
%T A285739 13429024118357421875,143533445691269324970571729935778225264543312,
%U A285739 91376242719004834465589805254054451484345405903423332764620213,25397841834482816377486479267527401525220329290217
%N A285739 Numerator of discriminant of n-th Bernoulli polynomial.
%H A285739 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BernoulliPolynomial.html">Bernoulli Polynomial</a>.
%H A285739 <a href="/index/Di#discriminants">Index entries for sequences related sequences related to discriminants of polynomials</a>.
%e A285739 1, 1/3, 1/16, 28/3375, 343/559872, 31/1815156, 29791/80621568, 178035712/124556484375, 11651995228221/80000000000000, ...
%e A285739 The first few Bernoulli polynomials are
%e A285739 0 | 1;
%e A285739 1 | x - 1/2;
%e A285739 2 | x^2 - x + 1/6;
%e A285739 3 | x^3 - 3*x^2/2 + x/2;
%e A285739 4 | x^4 - 2*x^3 + x^2 - 1/30;
%e A285739 5 | x^5 - 5*x^4/2 + 5*x^3/3 - x/6, etc.
%t A285739 Table[Numerator[Discriminant[BernoulliB[n, x], x]], {n, 1, 14}]
%o A285739 (PARI) a(n) = numerator(poldisc(bernpol(n))); \\ _Michel Marcus_, Mar 02 2023
%Y A285739 Cf. A053382, A053383, A196838, A196839, A285740 (denominators).
%K A285739 nonn,frac
%O A285739 1,4
%A A285739 _Ilya Gutkovskiy_, Apr 25 2017