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A020004 Nearest integer to Gamma(n + 1/12)/Gamma(1/12).

%I A020004 #20 Sep 08 2022 08:44:44
%S A020004 1,0,0,0,1,2,12,73,519,4193,38084,384010,4256112,51428023,672849973,
%T A020004 9475970455,142929221024,2298778304796,39270796040273,710146895061598,
%U A020004 13551969914092152,272168729108017393,5738224038694033364
%N A020004 Nearest integer to Gamma(n + 1/12)/Gamma(1/12).
%H A020004 G. C. Greubel, <a href="/A020004/b020004.txt">Table of n, a(n) for n = 0..445</a>
%e A020004 Gamma(0 + 1/12)/Gamma(1/12) = 1, so a(0) = 1.
%e A020004 Gamma(1 + 1/12)/Gamma(1/12) = 1/12 = 0.08333..., so a(1) = 0.
%e A020004 Gamma(2 + 1/12)/Gamma(1/12) = 13/144 < 1/2, so a(2) = 0.
%e A020004 Gamma(3 + 1/12)/Gamma(1/12) = 325/1728 < 1/2, so a(3) = 0.
%e A020004 Gamma(4 + 1/12)/Gamma(1/12) = 12025/20736 = 0.5799..., so a(4) = 1.
%e A020004 Gamma(5 + 1/12)/Gamma(1/12) = 589225/248832 = 2.3679631237..., so a(5) = 2.
%e A020004 Gamma(6 + 1/12)/Gamma(1/12) = 35942725/2985984 = 12.037145878879458..., so a(6) = 12.
%e A020004 Gamma(7 + 1/12)/Gamma(1/12) = 2623818925/35831808 = 73.22597..., so a(7) = 73.
%p A020004 Digits := 64:f := proc(n,x) round(GAMMA(n+x)/GAMMA(x)); end;
%t A020004 Table[Round[Gamma[n + 1/12]/Gamma[1/12]], {n, 0,50}] (* _G. C. Greubel_, Jan 19 2018 *)
%o A020004 (PARI) for(n=0,30, print1(round(gamma(n+1/12)/gamma(1/12)), ", ")) \\ _G. C. Greubel_, Jan 19 2018
%o A020004 (Magma) [Round(Gamma(n +1/12)/Gamma(1/12)): n in [0..30]]; // _G. C. Greubel_, Jan 19 2018
%Y A020004 Cf. A020049, A020094, A021016 (decimal expansion of 1/12), A203140 (decimal expansion of Gamma(1/12)).
%K A020004 nonn
%O A020004 0,6
%A A020004 _Simon Plouffe_