A020043 a(n) = round(Gamma(n+2/3)/Gamma(2/3)).

1, 1, 1, 3, 11, 51, 287, 1915, 14684, 127262, 1230202, 13122150, 153091745, 1939162101, 26501882045, 388694270000, 6089543563341, 101492392722343, 1793032271428052, 33469935733323642, 658242069422031619

Offset

0,4

Comments

Gamma(n+2/3)/Gamma(2/3) = {1, 2/3, 10/9, 80/27, 880/81, 12320/243, 209440/729, 4188800/2187, 96342400/6561, ...}. - R. J. Mathar, Sep 04 2016

Links

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

Maple

Digits := 64:f := proc(n, x) round(GAMMA(n+x)/GAMMA(x)); end;
seq(round(pochhammer(2/3, n)), n = 0..25); # G. C. Greubel, Dec 01 2019

Mathematica

Round[Pochhammer[2/3, Range[0, 25]]] (* G. C. Greubel, Dec 01 2019 *)

Prog

(PARI) x=2/3; vector(26, n, round(gamma(n-1+x)/gamma(x)) ) \\ G. C. Greubel, Dec 01 2019
(Magma) [Round(Gamma(n+2/3)/Gamma(2/3)): n in [0..25]]; // G. C. Greubel, Dec 01 2019
(Sage) [round(rising_factorial(2/3, n)) for n in (0..25)] # G. C. Greubel, Dec 01 2019

Crossrefs

Cf. A008544, A020088, A020133.

Sequence in context: A350354 A132006 A367011 * A357830 A184819 A113712

Adjacent sequences: A020040 A020041 A020042 * A020044 A020045 A020046

Keyword

nonn

Author

Simon Plouffe

Status

approved