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

Author

Simon Plouffe

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Cf. A008545, A020086, A020131.

Programs

Magma

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

Maple

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

Mathematica

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

PARI

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

Sage

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