A020044 a(n) = round(Gamma(n+1/3)/Gamma(1/3)).

1, 0, 0, 1, 3, 15, 80, 506, 3710, 30920, 288591, 2982109, 33797241, 416832633, 5557768440, 79661347641, 1221473997164, 19950741953682, 345812860530488, 6339902443058941, 122571447232472866, 2492286093726948268

Offset

0,5

Comments

Gamma(n+1/3)/Gamma(1/3) = {1, 1/3, 4/9, 28/27, 280/81, 3640/243, 58240/729, 1106560/2187, ...}. - 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(1/3, n)), n = 0..25); # G. C. Greubel, Dec 01 2019

Mathematica

Round[Pochhammer[1/3, Range[0, 25]]] (* G. C. Greubel, Dec 01 2019 *)

Prog

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

Crossrefs

Cf. A007559, A020089, A020134.

Sequence in context: A319216 A093889 A369085 * A024338 A253774 A003448

Adjacent sequences: A020041 A020042 A020043 * A020045 A020046 A020047

Keyword

nonn

Author

Simon Plouffe

Status

approved