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

0,4

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

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 *)

Prog

(PARI) x=3/4; vector(30, n, round(gamma(n-1+x)/gamma(x)) ) \\ G. C. Greubel, Dec 06 2019
(Magma) [Round(Gamma(n+3/4)/Gamma(3/4)): n in [0..30]]; // G. C. Greubel, Dec 06 2019
(Sage) [round(rising_factorial(3/4, n)) for n in (0..30)] # G. C. Greubel, Dec 06 2019

Crossrefs

Cf. A008545, A020086, A020131.

Sequence in context: A154407 A222467 A184265 * A081891 A119857 A305654

Adjacent sequences: A020038 A020039 A020040 * A020042 A020043 A020044

Keyword

nonn

Author

Simon Plouffe

Status

approved