A020042 a(n) = round( Gamma(n+1/4)/Gamma(1/4) ).

1, 0, 0, 1, 2, 10, 51, 319, 2310, 19061, 176310, 1807181, 20330789, 249052162, 3299941145, 47024161317, 717118460090, 11653174976468, 201017268344078, 3668565147279424, 70619879085128903, 1430052551473860293

Offset: 0

Author

Simon Plouffe

Keywords

• nonn

Comments

Gamma(n+1/4)/Gamma(1/4) = 1, 1/4, 5/16, 45/64, 585/256, 9945/1024, 208845/4096, 5221125/16384, 151412625/65536, ... - R. J. Mathar, Sep 04 2016

Links

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

Crossrefs

Cf. A007696, A020087, A020132.

Programs

Magma

[Round(Gamma(n+1/4)/Gamma(1/4)): 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(1/4,n)), n=0..30); # G. C. Greubel, Dec 06 2019

Mathematica

Table[Round[Pochhammer[1/4,n]], {n,0,30}] (* G. C. Greubel, Dec 06 2019 *)

PARI

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

Sage

[round(rising_factorial(1/4,n)) for n in (0..30)] # G. C. Greubel, Dec 06 2019