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A322508 Factorial expansion of Gamma(1/3) = Sum_{n>=1} a(n)/n!.

%I A322508 #9 May 24 2022 00:10:12
%S A322508 2,1,1,0,1,2,5,6,7,2,1,8,5,7,9,12,13,10,10,13,17,18,5,1,6,3,26,13,20,
%T A322508 29,8,31,27,19,21,27,5,14,12,3,9,37,34,40,14,29,35,12,27,4,36,22,24,
%U A322508 11,31,37,12,5,47,14,22,18,51,20,51,4,15,54,61,26,55,2,6,73,7,17,66,54,27
%N A322508 Factorial expansion of Gamma(1/3) = Sum_{n>=1} a(n)/n!.
%H A322508 <a href="https://oeis.org/index/Fa#facbase">Index entries for factorial base representation</a>
%e A322508 Gamma(1/3) = 2 + 1/2! + 1/3! + 0/4! + 1/5! + 2/6! + 5/7! + 6/8! + ...
%t A322508 With[{b = Gamma[1/3]}, Table[If[n==1, Floor[b], Floor[n!*b] - n*Floor[(n-1)!*b]], {n, 1, 100}]]
%o A322508 (PARI) default(realprecision, 250); b = gamma(1/3); for(n=1, 80, print1(if(n==1, floor(b), floor(n!*b) - n*floor((n-1)!*b)), ", "))
%o A322508 (Magma) SetDefaultRealField(RealField(250));  [Floor(Gamma(1/3))] cat [Floor(Factorial(n)*Gamma(1/3)) - n*Floor(Factorial((n-1))*Gamma(1/3)) : n in [2..80]];
%o A322508 (Sage)
%o A322508 b=gamma(1/3);
%o A322508 def a(n):
%o A322508     if (n==1): return floor(b)
%o A322508     else: return expand(floor(factorial(n)*b) -n*floor(factorial(n-1)*b))
%o A322508 [a(n) for n in (1..80)]
%Y A322508 Cf. A073005 (decimal expansion), A030651 (continued fraction).
%Y A322508 Cf. A068463 (Gamma(3/4)), A068464 (Gamma(1/4)), A322509 (Gamma(2/3)).
%K A322508 nonn
%O A322508 1,1
%A A322508 _G. C. Greubel_, Dec 12 2018