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.

A083591 Inverse binomial transform of A083589.

Original entry on oeis.org

1, 3, 9, 27, 82, 242, 736, 2188, 6600, 19736, 59328, 177744, 533728, 1600160, 4802560, 14403520, 43218816, 129640064, 388952832, 1166793216, 3500510464, 10501269248, 31504332544, 94511948032, 283537942272, 850609632512
Offset: 0

Views

Author

Paul Barry, May 02 2003

Keywords

Links

Crossrefs

Cf. A033139.

Programs

  • Mathematica
    LinearRecurrence[{-1,6,14,12},{1,3,9,27,82},30] (* Harvey P. Dale, Nov 04 2024 *)

Formula

O.g.f.: -(1+x)^4/[(2*x+1)(2*x^2+2*x+1)(-1+3*x)]. - R. J. Mathar, Apr 02 2008

A083590 Expansion of 1/((1-5*x)*(1-x^5)).

Original entry on oeis.org

1, 5, 25, 125, 625, 3126, 15630, 78150, 390750, 1953750, 9768751, 48843755, 244218775, 1221093875, 6105469375, 30527346876, 152636734380, 763183671900, 3815918359500, 19079591797500, 95397958987501, 476989794937505
Offset: 0

Views

Author

Paul Barry, May 02 2003

Keywords

Links

Crossrefs

Cf. A083589, A033139, A000975.

Programs

  • Magma
    [Floor(625*(5^(n+1)+1)/3124): n in [0..40]]; // G. C. Greubel, Oct 10 2017
  • Mathematica
    CoefficientList[Series[1/((1-5x)(1-x^5)),{x,0,40}],x] (* Vincenzo Librandi, Apr 04 2012 *)
LinearRecurrence[{5,0,0,0,1,-5},{1,5,25,125,625,3126},30] (* Harvey P. Dale, Jan 21 2023 *)
  • PARI
    Vec(1/(1-5*x)/(1-x^5)+O(x^99)) \\ Charles R Greathouse IV, Apr 04 2012

Formula

a(n) = floor(625*(5^(n+1)+1)/3124). - Tani Akinari, Jul 09 2013

A083592 Inverse binomial transform of A083590.

Original entry on oeis.org

1, 4, 16, 64, 256, 1025, 4095, 16395, 65545, 262250, 1048875, 4195700, 16782525, 67130375, 268521500, 1074085000, 4296343625, 17185365000, 68741481250, 274965882500, 1099863606875, 4399454303125, 17597817384375, 70391269365625
Offset: 0

Views

Author

Paul Barry, May 02 2003

Keywords

Links

Crossrefs

Cf. A083589.

Formula

O.g.f.: -(1+x)^5/[(1+5*x+10*x^2+10*x^3+5*x^4)(-1+4*x)]. - R. J. Mathar, Apr 02 2008
Showing 1-3 of 3 results.

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

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