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A090583
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Gosper's approximation to n!, sqrt((2*n+1/3)*Pi)*n^n/e^n, rounded to nearest integer.
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5
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1, 1, 2, 6, 24, 120, 720, 5039, 40316, 362851, 3628561, 39914615, 478979481, 6226774954, 87175314872, 1307635379670, 20922240412500, 355679137660826, 6402240370021199, 121642823201649058, 2432860847996122437, 51090157192742729183, 1123984974735953018069
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OFFSET
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0,3
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LINKS
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MAPLE
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Digits:= 2000;
a:= n-> round(sqrt((2*n+1/3)*Pi)*n^n/exp(n)):
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MATHEMATICA
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Join[{1}, Table[Round[Sqrt[(2*n + 1/3)*Pi]*n^n/Exp[n]], {n, 1, 50}]] (* G. C. Greubel, Nov 28 2017 *)
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PROG
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(PARI) a(n) = round(sqrt((2*n+1/3)*Pi)*n^n/exp(n)); \\ Bill McEachen, Aug 16 2014
(Magma) C<i> := ComplexField(); [Round(Sqrt((2*n + 1/3)*Pi(C))*n^n/Exp(n)): n in [0..30]]; // G. C. Greubel, Nov 28 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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