A020062 -id:A020062 - cp's OEIS frontend

A020060 a(n) = floor( Gamma(n+9/10)/Gamma(9/10) ).

1, 0, 1, 4, 19, 94, 559, 3857, 30477, 271252, 2685395, 29270806, 348322596, 4493361500, 62457724853, 930620100318, 14796859595058, 250066927156481, 4476197996101023, 84600142126309335, 1683542828313555774

Offset: 0

Simon Plouffe

nonn

G. C. Greubel, Table of n, a(n) for n = 0..445

Cf. A020015, A020105.

Cf. A020061, A020062, A020063.

[Floor(Gamma(n+9/10)/Gamma(9/10)): n in [0..20]]; // G. C. Greubel, Nov 13 2019

Digits := 64:f := proc(n,x) trunc(GAMMA(n+x)/GAMMA(x)); end;
seq(floor(pochhammer(9/10,n)), n = 0..20); # G. C. Greubel, Nov 13 2019

Floor[Pochhammer[9/10, Range[0, 20]]] (* G. C. Greubel, Nov 13 2019 *)

vector(21, n, my(x=9/10); gamma(n-1+x)\gamma(x) ) \\ G. C. Greubel, Nov 13 2019

[floor(rising_factorial(9/10, n)) for n in (0..20)] # G. C. Greubel, Nov 13 2019

A020017 Nearest integer to Gamma(n + 3/10)/Gamma(3/10).

Original entry on oeis.org

1, 0, 0, 1, 3, 13, 67, 425, 3103, 25751, 239483, 2466678, 27873456, 342843514, 4559818741, 65205407995, 997642742322, 16261576699844, 281325276907304, 5148252567403659, 99361274550890613, 2017033873383079454

Offset: 0

Simon Plouffe

nonn

Gamma(n + 3/10)/Gamma(3/10) = 1, 3/10, 39/100, 897/1000, 29601/10000, 1272843/100000, 67460679/1000000, ... - R. J. Mathar, Sep 04 2016

G. C. Greubel, Table of n, a(n) for n = 0..450

Cf. A020062, A020107.

[Round(Gamma(n+3/10)/Gamma(3/10)): n in [0..30]]; // G. C. Greubel, Jan 20 2018

Digits := 64:f := proc(n,x) round(GAMMA(n+x)/GAMMA(x)); end;

Table[Round[Gamma[n + 3/10]/Gamma[3/10]], {n, 0, 50}] (* G. C. Greubel, Jan 20 2018 *)

for(n=0,30, print1(round(gamma(n+3/10)/gamma(3/10)), ", ")) \\ G. C. Greubel, Jan 20 2018

A182831 Joint-rank array of numbers j*r^(i-1), where r=1+sqrt(2), read by antidiagonals.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 5, 11, 17, 22, 7, 14, 28, 45, 55, 9, 19, 37, 70, 112, 137, 10, 23, 48, 93, 171, 276, 334, 12, 26, 57, 118, 228, 417, 671, 812, 13, 31, 66, 141, 287, 556, 1010, 1627, 1965, 15, 34, 77, 164, 344, 697, 1347, 2444, 3934, 4751, 16, 39

Offset: 1

Clark Kimberling, Dec 07 2010

Joint-rank arrays are defined in the first comment at A182801. (row 1)=A087063. First 3 columns are A020062, A020063, A020064.

Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers.

			Northwest corner:
   1  2  4  5 ...
   3  6 11 14 ...
   8 17 28 37 ...
  22 45 70 93 ...
  ...

G. C. Greubel, Rows n=1..100 of triangle, flattened

Cf. A182801.

T[n_, k_] := Sum[Floor[k*(1 + Sqrt[2])^(n - j)], {j, 1, 100}]; Table[T[k + 1, n - k], {n,1,10}, {k, 0, n-1}]//Flatten (* G. C. Greubel, Aug 18 2018 *)

T(i,j) = Sum_{n>=1} floor(j*(1+sqrt(2))^(i-n)).

cp's OEIS Frontend

A020060 a(n) = floor( Gamma(n+9/10)/Gamma(9/10) ).

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A020017 Nearest integer to Gamma(n + 3/10)/Gamma(3/10).

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Author

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Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

A182831 Joint-rank array of numbers j*r^(i-1), where r=1+sqrt(2), read by antidiagonals.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula