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.

A335264 a(n) = Numerator(-4*n^2*Zeta(1 - n)^2*(1 - 2^n)) for n >= 1, a(0) = 0.

Original entry on oeis.org

0, 1, 1, 0, 1, 0, 1, 0, 17, 0, 775, 0, 477481, 0, 267589, 0, 3362251073, 0, 421424697891, 0, 38751520678991, 0, 44386209501802003, 0, 228891128457907983257, 0, 1636462395711601387189, 0, 348063222218272291910609213, 0, 3710225622968600411572814809525
Offset: 0

Views

Author

Peter Luschny, Jun 13 2020

Keywords

Examples

			Rational sequence starts: 0, 1, 1/3, 0, 1/15, 0, 1/7, 0, 17/15, 0, 775/33, 0, 477481/455, ...

Crossrefs

Cf. A335265 (denominators), A164555/A027642 (Bernoulli numbers).
Cf. A335538, A335539, A327497.

Programs

  • Maple
    a := s -> `if`(s = 0, 0, -4*s^2*Zeta(1 - s)^2*(1 - 2^s)):
seq(numer(a(s)), s = 0..24);

Formula

a(n) = numerator(Bernoulli(n)^2*(2^(n+2) - 4)).

A335265 a(n) = Denominator(-4*n^2*Zeta(1 - n)^2*(1 - 2^n)) for n >= 1, a(0) = 1.

Original entry on oeis.org

1, 1, 3, 1, 15, 1, 7, 1, 15, 1, 33, 1, 455, 1, 3, 1, 255, 1, 133, 1, 33, 1, 69, 1, 455, 1, 3, 1, 435, 1, 2387, 1, 255, 1, 3, 1, 319865, 1, 3, 1, 1353, 1, 43, 1, 345, 1, 141, 1, 7735
Offset: 0

Views

Author

Peter Luschny, Jun 13 2020

Keywords

Examples

			Rational sequence starts: 0, 1, 1/3, 0, 1/15, 0, 1/7, 0, 17/15, 0, 775/33, 0, 477481/455, ...

Crossrefs

Cf. A335264 (numerators), A164555/A027642 (Bernoulli numbers).
Cf. A335538, A335539, A327497.

Programs

  • Maple
    a := s -> `if`(s = 0, 0, -4*s^2*Zeta(1 - s)^2*(1 - 2^s)):
seq(denom(a(s)), s = 0..24);

Formula

a(n) = denominator(Bernoulli(n)^2*(2^(n+2) - 4)).

A335538 a(n) = numerator(-4*n^2*zeta(1 - n)*zeta(n)*(1 - 2^(1 - n)) / Pi^n) for n >= 2, a(0) = 0, a(1) = 1.

Original entry on oeis.org

0, 1, 1, 0, -7, 0, 31, 0, -127, 0, 365, 0, -977403607, 0, 57337, 0, -61240067209, 0, 252221719530919, 0, -15984987035583127, 0, 2841046127487821, 0, -468654557583574838590567, 0, 188822581306893585883, 0, -220710643004244238794643249, 0, 1594135539680034434970146279285311
Offset: 0

Views

Author

Peter Luschny, Jun 13 2020

Keywords

Examples

			Rational sequence starts: 0, 1, 1/9, 0, -7/1350, 0, 31/52920, 0, -127/1134000, 0, 365/11290752, ...

Crossrefs

Cf. A335539 (denominators), A164555/A027642 (Bernoulli numbers).
Cf. A335264, A335265, A327497.

Programs

  • Maple
    a := s -> `if`(s=1 or s=0, s, -4*s^2*Zeta(1 - s)*Zeta(s)*(1 - 2^(1 - s)) / Pi^s):
seq(numer(a(s)), s = 0..34);

Formula

a(n) = numerator(n*Bernoulli(n)*zeta(n)*(4-2^(3-n))/Pi^n) for n >= 2.
Showing 1-3 of 3 results.

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

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