A285739 Numerator of discriminant of n-th Bernoulli polynomial.

1, 1, 1, 28, 343, 31, 29791, 178035712, 11651995228221, 1087618835548371875, 13429024118357421875, 143533445691269324970571729935778225264543312, 91376242719004834465589805254054451484345405903423332764620213, 25397841834482816377486479267527401525220329290217

Offset: 1

Author

Ilya Gutkovskiy, Apr 25 2017

Keywords

• nonn
• frac

Examples

			1, 1/3, 1/16, 28/3375, 343/559872, 31/1815156, 29791/80621568, 178035712/124556484375, 11651995228221/80000000000000, ...
The first few Bernoulli polynomials are
0 | 1;
1 | x - 1/2;
2 | x^2 - x + 1/6;
3 | x^3 - 3*x^2/2 + x/2;
4 | x^4 - 2*x^3 + x^2 - 1/30;
5 | x^5 - 5*x^4/2 + 5*x^3/3 - x/6, etc.
		

Links

• Eric Weisstein's World of Mathematics, Bernoulli Polynomial.
• Index entries for sequences related sequences related to discriminants of polynomials.

Crossrefs

Cf. A053382, A053383, A196838, A196839, A285740 (denominators).

Programs

Mathematica

Table[Numerator[Discriminant[BernoulliB[n, x], x]], {n, 1, 14}]

PARI

a(n) = numerator(poldisc(bernpol(n))); \\ Michel Marcus, Mar 02 2023