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.

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A381198 a(n) = denominator( [(x*y*z*u)^n] 1/sqrt(1 - (x + y + z + u*(x*y + x*z + y*z))) ).

Original entry on oeis.org

1, 4, 64, 256, 16384, 65536, 1048576, 4194304, 1073741824, 4294967296, 68719476736, 274877906944, 17592186044416, 70368744177664, 1125899906842624, 4503599627370496, 4611686018427387904, 18446744073709551616, 295147905179352825856, 1180591620717411303424, 75557863725914323419136
Offset: 0

Views

Author

Stefano Spezia, Feb 16 2025

Keywords

Comments

Apparently a duplicate of A110258 and A056982. - R. J. Mathar, Feb 18 2025

Links

Crossrefs

Cf. A268554, A381197 (numerators).

Programs

  • Mathematica
    a[n_]:=Denominator[SeriesCoefficient[1/Sqrt[1-(x+y+z+u*(x*y+x*z+y*z))],{x,0,n},{y,0,n},{z,0,n},{u,0,n}]]; Array[a,15,0]

A212298 Decimal expansion of (gamma + log(16))/Pi.

Original entry on oeis.org

1, 0, 6, 6, 2, 7, 5, 8, 5, 3, 2, 0, 8, 9, 1, 4, 3, 5, 4, 3, 4, 5, 1, 1, 0, 1, 9, 6, 6, 1, 5, 7, 4, 6, 9, 4, 6, 7, 5, 8, 0, 1, 7, 5, 5, 6, 0, 3, 9, 9, 0, 4, 3, 0, 6, 6, 7, 9, 2, 2, 7, 3, 5, 1, 5, 7, 7, 6, 1, 2, 7, 0, 6, 8, 8, 5, 9, 8, 2, 8, 7, 1, 2, 5, 0, 4, 4
Offset: 1

Views

Author

Charles R Greathouse IV, Jul 02 2012

Keywords

Comments

Decimal expansion of c, where G_n = A277233(n)/A056982(n) = c + log(n+1)/Pi - 1/(4 Pi(n+1)) + O(1/n^2). [Corrected by Peter Luschny, Sep 27 2019]
Decimal expansion of c, where G_n = A277233(n)/A056982(n) = c + log(n+3/4)/Pi + O(1/n^2). - Peter Luschny, Sep 27 2019

Examples

			1.06627585320891435434511019661574694675801755603990430667922735157761...

References

  • Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 4.2.1, p. 252.

Links

Crossrefs

Cf. A277233/A056982.

Programs

  • Maple
    Digits := 120: ((gamma + 4*log(2))/Pi)*10^94:
ListTools:-Reverse(convert(floor(%), base, 10)); # Peter Luschny, Sep 27 2019
  • Mathematica
    RealDigits[(EulerGamma + Log[16])/Pi, 10, 87][[1]] (* Georg Fischer, Apr 04 2020 *)
  • PARI
    (Euler+log(16))/Pi

Extensions

Definition amended by Georg Fischer, Apr 04 2020

A358695 a(n) = numerator( Sum_{k=0..n} (-1)^k * binomial(1/2, k)^2 * binomial(n, k) ).

Original entry on oeis.org

1, 3, 33, 75, 1305, -8253, -340711, -2173509, -758532375, -3823240245, -73518428511, -342444310533, -24952606638687, -111735599023125, -1975318542049815, -8639356601706213, -9590905885722547959, -41296955508208952901, -707029904720030040775, -3010762771187568788685
Offset: 0

Views

Author

Peter Luschny, Dec 08 2022

Keywords

Crossrefs

Cf. A056982 (denominators), A260832, A358113.

Programs

  • Maple
    a := n -> numer(simplify(hypergeom([-1/2, -1/2, -n], [1, 1], 1))):
seq(a(n), n = 0..19);
  • Mathematica
    a[n_] := Numerator[HypergeometricPFQ[{-1/2, -1/2, -n}, {1, 1}, 1]]; Array[a, 20, 0] (* Amiram Eldar, Dec 08 2022 *)

Formula

a(n) = numerator(hypergeometric([-1/2, -1/2, -n], [1, 1], 1)).
a(n) = numerator(A358113(n) / 16^n). - Andrey Zabolotskiy, Dec 08 2022
Previous Showing 31-33 of 33 results.

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

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