A285740 Denominator of discriminant of n-th Bernoulli polynomial.
1, 3, 16, 3375, 559872, 1815156, 80621568, 124556484375, 80000000000000, 11881340006899968, 1218719480020992, 3405780508865246682482292626953125, 1526226812966134209666905971200000000000000000, 18160335421875000000000000
Offset: 1
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.
Programs
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Mathematica
Table[Denominator[Discriminant[BernoulliB[n, x], x]], {n, 1, 14}] -
PARI
a(n) = denominator(poldisc(bernpol(n))); \\ Michel Marcus, Mar 02 2023