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A020045
Nearest integer to Gamma(n + 1/2)/Gamma(1/2).
2
1, 1, 1, 2, 7, 30, 162, 1056, 7918, 67304, 639384, 6713531, 77205601, 965070017, 13028445232, 188912455860, 2928143065834, 48314360586264, 845501310259627, 15641774239803107, 305014597676160594, 6252799252361292173
OFFSET
0,4
COMMENTS
Gamma(n + 1/2)/Gamma(1/2) = 1, 1/2, 3/4, 15/8, 105/16, 945/32, 10395/64, 135135/128, 2027025/256, 34459425/512, ... - R. J. Mathar, Sep 04 2016
LINKS
FORMULA
Also nearest integer (where .5 is rounded up) to (2n)!/(n!*2^(2n)) or A001813(n)/A000302(n). - Gerald McGarvey, Jan 20 2005
MAPLE
Digits := 64:f := proc(n, x) round(GAMMA(n+x)/GAMMA(x)); end;
MATHEMATICA
Join[{1, 1}, Table[Round[Pochhammer[1/2, n]], {n, 2, 30}]] (* G. C. Greubel, Nov 19 2018 *)
PROG
(PARI) default(realprecision, 100); for(n=0, 30, print1(round(gamma(n+1/2)/gamma(1/2)), ", ")) \\ G. C. Greubel, Nov 19 2018
(Magma) [Round(Gamma(n + 1/2)/Gamma(1/2)): n in [0..30]]; // G. C. Greubel, Nov 19 2018
(Sage) [round(gamma(n+1/2)/gamma(1/2)) for n in range(30)] # G. C. Greubel, Nov 19 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved