A020018 Nearest integer to Gamma(n + 1/10)/Gamma(1/10).

1, 0, 0, 0, 1, 3, 15, 91, 649, 5253, 47802, 482796, 5359036, 64844333, 849460756, 11977396665, 180858689642, 2911824903230, 49792205845229, 901238925798638, 17213663482753993, 345994636003355265, 7300486819670796088

Offset: 0

Author

Simon Plouffe

Keywords

• nonn

Examples

			Gamma(1/10)/Gamma(1/10) = 1, so a(0) = 1.
Gamma(1 + 1/10)/Gamma(1/10) = 1/10 < 1/2, so a(1) = 0.
Gamma(2 + 1/10)/Gamma(1/10) = 11/100 < 1/2, so a(2) = 0.
Gamma(3 + 1/10)/Gamma(1/10) = 231/1000 < 1/2, so a(3) = 0.
Gamma(4 + 1/10)/Gamma(1/10) = 7161/10000 = 0.7161, so a(4) = 1.
Gamma(5 + 1/10)/Gamma(1/10) = 293601/100000 = 2.93601, so a(5) = 3.
Gamma(6 + 1/10)/Gamma(1/10) = 14973651/1000000 = 14.973651, so a(6) = 15.
		

Links

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

Crossrefs

Cf. A045757, A020063, A020108, A000007 (decimal expansion of 1/10), A256191 (decimal expansion of Gamma(1/10)).

Programs

Magma

[Round(Gamma(n +1/10)/Gamma(1/10)): n in [0..30]]; // G. C. Greubel, Jan 20 2018

Maple

Digits := 64:f := proc(n,x) round(GAMMA(n+x)/GAMMA(x)); end;

Mathematica

Table[Round[Gamma[n + 1/10]/Gamma[1/10]], {n, 0, 50}] (* G. C. Greubel, Jan 20 2018 *)

PARI

for(n=0,30, print1(round(gamma(n+1/10)/gamma(1/10)), ", ")) \\ G. C. Greubel, Jan 20 2018