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A322509 Factorial expansion of Gamma(2/3) = Sum_{n>=1} a(n)/n!.

%I A322509 #9 May 24 2022 00:10:04
%S A322509 1,0,2,0,2,2,6,6,0,3,1,11,7,6,6,14,1,8,12,15,8,17,8,1,13,15,3,4,10,16,
%T A322509 25,1,25,22,6,3,19,17,8,10,25,37,29,17,35,19,24,25,30,31,4,7,51,49,14,
%U A322509 51,45,54,0,26,34,41,56,57,16,15,63,4,51,42,13,35,12,15,66,22,13,43,14,78
%N A322509 Factorial expansion of Gamma(2/3) = Sum_{n>=1} a(n)/n!.
%H A322509 <a href="https://oeis.org/index/Fa#facbase">Index entries for factorial base representation</a>
%e A322509 Gamma(2/3) = 1 + 0/2! + 2/3! + 0/4! + 2/5! + 2/6! + 6/7! + 6/8! + ...
%t A322509 With[{b = Gamma[2/3]}, Table[If[n == 1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]]
%o A322509 (PARI) default(realprecision, 250); b = gamma(2/3); for(n=1, 80, print1(if(n==1, floor(b), floor(n!*b) - n*floor((n-1)!*b)), ", "))
%o A322509 (Magma) SetDefaultRealField(RealField(250));  [Floor(Gamma(2/3))] cat [Floor(Factorial(n)*Gamma(2/3)) - n*Floor(Factorial((n-1))*Gamma(2/3)) : n in [2..80]];
%o A322509 (Sage)
%o A322509 b=gamma(2/3);
%o A322509 def a(n):
%o A322509     if (n==1): return floor(b)
%o A322509     else: return expand(floor(factorial(n)*b) -n*floor(factorial(n-1)*b))
%o A322509 [a(n) for n in (1..80)]
%Y A322509 Cf. A073006 (decimal expansion), A030652 (continued fraction).
%Y A322509 Cf. A068463 (Gamma(3/4)), A068464 (Gamma(1/4)), A322508 (Gamma(1/3)).
%K A322509 nonn
%O A322509 1,3
%A A322509 _G. C. Greubel_, Dec 12 2018