A020131 -id:A020131 - cp's OEIS frontend

A020041 a(n) = round( Gamma(n+3/4)/Gamma(3/4) ).

1, 1, 1, 4, 14, 64, 370, 2495, 19339, 169215, 1649844, 17735823, 208395916, 2657047924, 36534408953, 538882532061, 8487399879954, 142163947989232, 2523410076808877, 47313938940166438, 934450294068287158

Offset: 0

Simon Plouffe

nonn

Gamma(n+3/4)/Gamma(3/4) = 1, 3/4, 21/16, 231/64, 3465/256, 65835/1024, 1514205/4096, 40883535/16384, 1267389585/65536, ... - R. J. Mathar, Sep 04 2016

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

Cf. A008545, A020086, A020131.

[Round(Gamma(n+3/4)/Gamma(3/4)): n in [0..30]]; // G. C. Greubel, Dec 06 2019

Digits := 64:f := proc(n,x) round(GAMMA(n+x)/GAMMA(x)); end;
seq( round(pochhammer(3/4,n)), n=0..30); # G. C. Greubel, Dec 06 2019

Table[Round[Pochhammer[3/4,n]], {n,0,30}] (* G. C. Greubel, Dec 06 2019 *)

x=3/4; vector(30, n, round(gamma(n-1+x)/gamma(x)) ) \\ G. C. Greubel, Dec 06 2019

[round(rising_factorial(3/4,n)) for n in (0..30)] # G. C. Greubel, Dec 06 2019

A020086 a(n) = floor( Gamma(n + 3/4)/Gamma(3/4) ).

Original entry on oeis.org

1, 0, 1, 3, 13, 64, 369, 2495, 19338, 169214, 1649843, 17735822, 208395915, 2657047923, 36534408953, 538882532060, 8487399879954, 142163947989232, 2523410076808876, 47313938940166438, 934450294068287157

Offset: 0

Simon Plouffe

nonn

G. C. Greubel, Table of n, a(n) for n = 0..449

Cf. A020041, A020131.

[Truncate(Gamma(n + 3/4)/Gamma(3/4)): n in [0..30]]; // G. C. Greubel, Nov 19 2018

Digits:= 64: x:=3/4: f := proc(n,x) trunc(GAMMA(n+x)/GAMMA(x)); end;
seq(floor(pochhammer(3/4,n)), n = 0..25); # G. C. Greubel, Nov 17 2019

Floor[Pochhammer[3/4, Range[0, 25]]] (* G. C. Greubel, Nov 19 2018 *)

vector(26, n, my(x=3/4); gamma(n-1+x)\gamma(x) ) \\ G. C. Greubel, Nov 19 2018

[int(gamma(n + 3/4)/gamma(3/4))  for n in range(30)] # G. C. Greubel, Nov 19 2018

cp's OEIS Frontend

A020041 a(n) = round( Gamma(n+3/4)/Gamma(3/4) ).

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