A020113 - OEIS

%I #21 Sep 08 2022 08:44:45

%S 1,1,1,1,2,9,43,267,1928,15845,146123,1493701,16762640,204876709,

%T 2708925369,38526938569,586465620431,9513775620310,163848357905336,

%U 2985681188497228,57391427290002262,1160582196308934616,24630133277222945727,547336295049398793928

%N a(n) = ceiling of Gamma(n + 2/9)/Gamma(2/9).

%F a(n) ~ sqrt(2*Pi)*n^(n-5/18)*exp(-n)/Gamma(2/9) as n -> infinity. - _Robert Israel_, Jun 07 2015

%e Gamma(6 + 2/9) = 176.09917208972649...

%e Gamma(2/9) = 4.1065795667...

%e 176.09917208972649.../4.1065795667... = 42.8822... hence a(6) = 43.

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

%t Table[Ceiling[Gamma[n + 2/9]/Gamma[2/9]], {n, 0, 19}] (* _Alonso del Arte_, Jun 07 2015 *)

%o (Magma) [Ceiling(Gamma(n + 2/9)/Gamma(2/9)): n in [0..30]]; // _Vincenzo Librandi_, Jun 08 2015

%K nonn

%O 0,5

%A _Simon Plouffe_