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

1, 0, 0, 0, 1, 2, 12, 73, 519, 4193, 38084, 384010, 4256112, 51428023, 672849973, 9475970455, 142929221024, 2298778304796, 39270796040273, 710146895061598, 13551969914092152, 272168729108017393, 5738224038694033364

Offset: 0

Author

Simon Plouffe

Keywords

• nonn

Examples

			Gamma(0 + 1/12)/Gamma(1/12) = 1, so a(0) = 1.
Gamma(1 + 1/12)/Gamma(1/12) = 1/12 = 0.08333..., so a(1) = 0.
Gamma(2 + 1/12)/Gamma(1/12) = 13/144 < 1/2, so a(2) = 0.
Gamma(3 + 1/12)/Gamma(1/12) = 325/1728 < 1/2, so a(3) = 0.
Gamma(4 + 1/12)/Gamma(1/12) = 12025/20736 = 0.5799..., so a(4) = 1.
Gamma(5 + 1/12)/Gamma(1/12) = 589225/248832 = 2.3679631237..., so a(5) = 2.
Gamma(6 + 1/12)/Gamma(1/12) = 35942725/2985984 = 12.037145878879458..., so a(6) = 12.
Gamma(7 + 1/12)/Gamma(1/12) = 2623818925/35831808 = 73.22597..., so a(7) = 73.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..445

Crossrefs

Cf. A020049, A020094, A021016 (decimal expansion of 1/12), A203140 (decimal expansion of Gamma(1/12)).

Programs

Magma

[Round(Gamma(n +1/12)/Gamma(1/12)): n in [0..30]]; // G. C. Greubel, Jan 19 2018

Maple

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

Mathematica

Table[Round[Gamma[n + 1/12]/Gamma[1/12]], {n, 0,50}] (* G. C. Greubel, Jan 19 2018 *)

PARI

for(n=0,30, print1(round(gamma(n+1/12)/gamma(1/12)), ", ")) \\ G. C. Greubel, Jan 19 2018