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 1-6 of 6 results.

A020064 Integer part of Gamma(n+8/9)/Gamma(8/9).

Original entry on oeis.org

1, 0, 1, 4, 18, 92, 543, 3741, 29513, 262341, 2594261, 28248627, 335844792, 4328666215, 60120364100, 895125421053, 14222548356738, 240203038913807, 4296965473902563, 81164903395937306, 1614279745319197538
Offset: 0

Views

Author

Simon Plouffe

Keywords

Links

Crossrefs

Cf. A020065, A020066, A020067, A020068, A020069.
Cf. A020019, A020109.

Programs

  • Magma
    [Truncate(Gamma(n+8/9)/Gamma(8/9)): n in [0..20]]; // G. C. Greubel, Nov 13 2019
  • Maple
    Digits := 64:f := proc(n,x) trunc(GAMMA(n+x)/GAMMA(x)); end;
seq(trunc(pochhammer(8/9,n)), n = 0..20); # G. C. Greubel, Nov 13 2019
  • Mathematica
    IntegerPart[Pochhammer[8/9, Range[0, 20]]] (* G. C. Greubel, Nov 13 2019 *)
  • PARI
    P(n,x) = gamma(x+n)/gamma(x);
vector(21, n, truncate(P(n-1, 8/9)) ) \\ G. C. Greubel, Nov 13 2019
  • Sage
    [int(rising_factorial(8/9, n)) for n in (0..20)] # G. C. Greubel, Nov 13 2019

A020066 Integer part of Gamma(n+5/9)/Gamma(5/9).

Original entry on oeis.org

1, 0, 0, 2, 7, 35, 198, 1302, 9843, 84216, 804738, 8494460, 98158213, 1232430908, 16706285646, 243169268856, 3782633071103, 62623591954942, 1099391947653437, 20399828362013787, 398929976857158503
Offset: 0

Views

Author

Simon Plouffe

Keywords

Links

Crossrefs

Cf. A020064, A020065, A020067, A020068, A020069.
Cf. A020021, A020111.

Programs

  • Magma
    [Truncate(Gamma(n+5/9)/Gamma(5/9)): n in [0..20]]; // G. C. Greubel, Nov 13 2019
  • Maple
    Digits := 64:f := proc(n,x) trunc(GAMMA(n+x)/GAMMA(x)); end;
seq(trunc(pochhammer(5/9,n)), n = 0..20); # G. C. Greubel, Nov 13 2019
  • Mathematica
    IntegerPart[Pochhammer[5/9, Range[0, 20]]] (* G. C. Greubel, Nov 13 2019 *)
  • PARI
    P(n,x) = gamma(x+n)/gamma(x);
vector(21, n, truncate(P(n-1, 5/9)) ) \\ G. C. Greubel, Nov 13 2019
  • Sage
    [int(rising_factorial(5/9, n)) for n in (0..20)] # G. C. Greubel, Nov 13 2019

A020067 Integer part of Gamma(n+4/9)/Gamma(4/9).

Original entry on oeis.org

1, 0, 0, 1, 5, 24, 130, 842, 6274, 52988, 500442, 5226841, 59818300, 744405515, 10008118594, 144561713037, 2232675345794, 36715105686390, 640474621418148, 11813198572823622, 229701083360459334, 4696111037591613052
Offset: 0

Views

Author

Simon Plouffe

Keywords

Links

Crossrefs

Cf. A020064, A020065, A020066, A020068, A020069.
Cf. A020022, A020112.

Programs

  • Magma
    [Truncate(Gamma(n+4/9)/Gamma(4/9)): n in [0..25]]; // G. C. Greubel, Nov 13 2019
  • Maple
    Digits := 64:f := proc(n,x) trunc(GAMMA(n+x)/GAMMA(x)) end: seq(f(n,4/9), n=0..25);
# alternative:
seq(trunc(pochhammer(4/9,n)), n = 0..25); # G. C. Greubel, Nov 13 2019
  • Mathematica
    IntegerPart[Pochhammer[4/9, Range[0, 25]]] (* G. C. Greubel, Nov 13 2019 *)
  • PARI
    P(n,x) = gamma(x+n)/gamma(x);
vector(26, n, truncate(P(n-1, 4/9)) ) \\ G. C. Greubel, Nov 13 2019
  • Sage
    [int(rising_factorial(4/9, n)) for n in (0..25)] # G. C. Greubel, Nov 13 2019

A020068 a(n) = floor( Gamma(n+2/9) / Gamma(2/9) ).

Original entry on oeis.org

1, 0, 0, 0, 1, 8, 42, 266, 1927, 15844, 146122, 1493700, 16762639, 204876708, 2708925368, 38526938568, 586465620430, 9513775620309, 163848357905335, 2985681188497227, 57391427290002261, 1160582196308934615
Offset: 0

Views

Author

Simon Plouffe

Keywords

Links

Crossrefs

Cf. A020064, A020065, A020066, A020067, A020069.
Cf. A020023, A020113.

Programs

  • Magma
    [Floor(Gamma(n+2/9)/Gamma(2/9)): n in [0..25]]; // G. C. Greubel, Nov 13 2019
  • Maple
    Digits := 64:f := proc(n,x) trunc(GAMMA(n+x)/GAMMA(x)); end;
seq(floor(pochhammer(2/9,n)), n = 0..25); # G. C. Greubel, Nov 13 2019
  • Mathematica
    Floor[Pochhammer[2/9, Range[0, 25]]] (* G. C. Greubel, Nov 13 2019 *)
  • PARI
    x=2/9; vector(26, n, gamma(n-1+x)\gamma(x) ) \\ G. C. Greubel, Nov 13 2019
  • Sage
    [floor(rising_factorial(2/9, n)) for n in (0..25)] # G. C. Greubel, Nov 13 2019

A020069 Integer part of Gamma(n+1/9)/Gamma(1/9).

Original entry on oeis.org

1, 0, 0, 0, 0, 3, 17, 104, 740, 6005, 54717, 553253, 6147263, 74450193, 976124760, 13774204958, 208143541601, 3353423725801, 57380805974819, 1039230152655057, 19860842917407765, 399423618672311729
Offset: 0

Views

Author

Simon Plouffe

Keywords

Links

Crossrefs

Cf. A020064, A020065, A020066, A020067, A020068.
Cf. A020024, A020114.

Programs

  • Magma
    [Truncate(Gamma(n+1/9)/Gamma(1/9)): n in [0..25]]; // G. C. Greubel, Nov 13 2019
  • Maple
    Digits := 64:f := proc(n,x) trunc(GAMMA(n+x)/GAMMA(x)); end;
seq(trunc(pochhammer(1/9,n)), n = 0..25); # G. C. Greubel, Nov 13 2019
  • Mathematica
    IntegerPart[Pochhammer[1/9, Range[0, 25]]] (* G. C. Greubel, Nov 13 2019 *)
  • PARI
    P(n,x) = gamma(x+n)/gamma(x);
vector(26, n, truncate(P(n-1, 1/9)) ) \\ G. C. Greubel, Nov 13 2019
  • Sage
    [int(rising_factorial(1/9, n)) for n in (0..25)] # G. C. Greubel, Nov 13 2019

A020020 Nearest integer to Gamma(n + 7/9)/Gamma(7/9).

Original entry on oeis.org

1, 1, 1, 4, 15, 69, 401, 2715, 21115, 185345, 1812263, 19532171, 230045569, 2939471158, 40499380397, 598490843643, 9442855533027, 158430131720783, 2816535675036147, 52888281009012092, 1046012668844905826
Offset: 0

Views

Author

Simon Plouffe

Keywords

Comments

Gamma(n + 7/9)/Gamma(7/9) = 1, 7/9, 112/81, 2800/729, 95200/6561, 4093600/59049, 212867200/531441, 12984899200/4782969, ... - R. J. Mathar, Sep 04 2016

Links

Crossrefs

Cf. A020065, A020110.

Programs

  • Magma
    [Round(Gamma(n +7/9)/Gamma(7/9)): n in [0..30]]; // G. C. Greubel, Feb 03 2018
  • Maple
    Digits := 64:f := proc(n,x) round(GAMMA(n+x)/GAMMA(x)); end;
  • Mathematica
    Table[Round[Gamma[n + 7/9]/Gamma[7/9]], {n, 0, 50}] (* G. C. Greubel, Feb 03 2018 *)
  • PARI
    for(n=0,30, print1(round(gamma(n+7/9)/gamma(7/9)), ", ")) \\ G. C. Greubel, Feb 03 2018
Showing 1-6 of 6 results.

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

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