cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A366152 a(n) = denominator(denominator(Bernoulli'(n, x)) / denominator(Bernoulli(n, 1))).

Original entry on oeis.org

1, 2, 6, 1, 30, 1, 42, 1, 10, 1, 66, 1, 2730, 1, 2, 1, 170, 1, 798, 1, 110, 1, 46, 1, 546, 1, 2, 1, 870, 1, 14322, 1, 170, 1, 2, 1, 1919190, 1, 2, 1, 4510, 1, 1806, 1, 46, 1, 94, 1, 1326, 1, 22, 1, 530, 1, 798, 1, 290, 1, 118, 1, 56786730, 1, 2, 1, 34, 1, 64722
Offset: 0

Views

Author

Peter Luschny, Oct 13 2023

Keywords

Crossrefs

Cf. A324370/A027642, A366570 (numerator), A366426/A366427 (2nd derivative).

Programs

  • Maple
    seq(denom(denom(diff(bernoulli(n, x), x))/denom(bernoulli(n, 1))), n = 0..66);
  • PARI
    a(n) = denominator(lcm(apply(denominator, Vec(deriv(bernpol(n)))))/denominator(subst(bernpol(n, x), x, 1))); \\ Michel Marcus, Oct 14 2023

Formula

a(n) = denominator(A324370(n) / A027642(n)).

A366426 a(n) = numerator(denominator(Bernoulli''(n, x)) / denominator(Bernoulli(n, 1))).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 3, 5, 5, 7, 1, 5, 15, 1, 1, 7, 7, 1, 1, 1, 1, 77, 7, 35, 3, 1, 1, 455, 35, 7, 21, 55, 55, 7, 7, 7, 105, 1, 5, 221, 13, 11, 33, 55, 1, 19, 1, 5, 15, 1, 1, 5005, 715, 143, 33, 17, 85, 161, 35, 1, 3, 11, 55, 95095
Offset: 0

Views

Author

Peter Luschny, Oct 13 2023

Keywords

Crossrefs

Cf. A366168/A027642, A366427 (denominator), A366570/A366152 (1st derivative).

Programs

  • Maple
    seq(numer(denom(diff(diff(bernoulli(n, x), x),x))/denom(bernoulli(n, 1))), n = 0..75);
  • PARI
    a(n) = numerator(lcm(apply(denominator, Vec(deriv(deriv(bernpol(n))))))/denominator(subst(bernpol(n, x), x, 1))); \\ Michel Marcus, Oct 14 2023

Formula

a(n) = numerator(A366168(n) / A027642(n)).

A366570 a(n) = numerator(denominator(Bernoulli'(n, x)) / denominator(Bernoulli(n, 1))).

Original entry on oeis.org

1, 1, 1, 2, 1, 6, 1, 6, 1, 10, 1, 6, 1, 210, 5, 2, 1, 30, 5, 210, 7, 110, 5, 30, 1, 546, 7, 14, 1, 30, 1, 462, 77, 1190, 35, 6, 1, 51870, 455, 70, 7, 2310, 55, 2310, 7, 322, 35, 210, 1, 6630, 221, 286, 11, 330, 55, 798, 19, 290, 5, 30, 1, 930930, 5005, 1430
Offset: 0

Views

Author

Peter Luschny, Oct 13 2023

Keywords

Crossrefs

Cf. A324370/A027642, A366152 (denominator), A366426/A366427 (2nd derivative).

Programs

  • Maple
    seq(numer(denom(diff(bernoulli(n, x), x))/denom(bernoulli(n, 1))), n = 0..66);
  • PARI
    a(n) = numerator(lcm(apply(denominator, Vec(deriv(bernpol(n)))))/denominator(subst(bernpol(n, x), x, 1))); \\ Michel Marcus, Oct 14 2023

Formula

a(n) = numerator(A324370(n) / A027642(n)).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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