A020113 a(n) = ceiling of Gamma(n + 2/9)/Gamma(2/9).

1, 1, 1, 1, 2, 9, 43, 267, 1928, 15845, 146123, 1493701, 16762640, 204876709, 2708925369, 38526938569, 586465620431, 9513775620310, 163848357905336, 2985681188497228, 57391427290002262, 1160582196308934616, 24630133277222945727, 547336295049398793928

Offset: 0

Author

Simon Plouffe

Keywords

• nonn

Examples

			Gamma(6 + 2/9) = 176.09917208972649...
Gamma(2/9) = 4.1065795667...
176.09917208972649.../4.1065795667... = 42.8822... hence a(6) = 43.
		

Programs

Magma

[Ceiling(Gamma(n + 2/9)/Gamma(2/9)): n in [0..30]]; // Vincenzo Librandi, Jun 08 2015

Maple

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

Mathematica

Table[Ceiling[Gamma[n + 2/9]/Gamma[2/9]], {n, 0, 19}] (* Alonso del Arte, Jun 07 2015 *)

Formula

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