cp's OEIS Frontend

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

%I A020018 #20 Sep 08 2022 08:44:44
%S A020018 1,0,0,0,1,3,15,91,649,5253,47802,482796,5359036,64844333,849460756,
%T A020018 11977396665,180858689642,2911824903230,49792205845229,
%U A020018 901238925798638,17213663482753993,345994636003355265,7300486819670796088
%N A020018 Nearest integer to Gamma(n + 1/10)/Gamma(1/10).
%H A020018 G. C. Greubel, <a href="/A020018/b020018.txt">Table of n, a(n) for n = 0..450</a>
%e A020018 Gamma(1/10)/Gamma(1/10) = 1, so a(0) = 1.
%e A020018 Gamma(1 + 1/10)/Gamma(1/10) = 1/10 < 1/2, so a(1) = 0.
%e A020018 Gamma(2 + 1/10)/Gamma(1/10) = 11/100 < 1/2, so a(2) = 0.
%e A020018 Gamma(3 + 1/10)/Gamma(1/10) = 231/1000 < 1/2, so a(3) = 0.
%e A020018 Gamma(4 + 1/10)/Gamma(1/10) = 7161/10000 = 0.7161, so a(4) = 1.
%e A020018 Gamma(5 + 1/10)/Gamma(1/10) = 293601/100000 = 2.93601, so a(5) = 3.
%e A020018 Gamma(6 + 1/10)/Gamma(1/10) = 14973651/1000000 = 14.973651, so a(6) = 15.
%p A020018 Digits := 64:f := proc(n,x) round(GAMMA(n+x)/GAMMA(x)); end;
%t A020018 Table[Round[Gamma[n + 1/10]/Gamma[1/10]], {n, 0, 50}] (* _G. C. Greubel_, Jan 20 2018 *)
%o A020018 (PARI) for(n=0,30, print1(round(gamma(n+1/10)/gamma(1/10)), ", ")) \\ _G. C. Greubel_, Jan 20 2018
%o A020018 (Magma) [Round(Gamma(n +1/10)/Gamma(1/10)): n in [0..30]]; // _G. C. Greubel_, Jan 20 2018
%Y A020018 Cf. A045757, A020063, A020108, A000007 (decimal expansion of 1/10), A256191 (decimal expansion of Gamma(1/10)).
%K A020018 nonn
%O A020018 0,6
%A A020018 _Simon Plouffe_