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A067277 Factorial expansion of zeta(3): zeta(3) = Sum_{n>=1} a(n)/n!.

%I A067277 #12 Sep 08 2022 08:45:05
%S A067277 1,0,1,0,4,1,3,2,8,4,0,11,11,10,9,4,2,11,5,12,16,12,6,3,22,22,12,14,
%T A067277 23,1,24,24,12,14,1,27,14,26,21,16,22,14,6,19,12,12,36,22,32,38,10,1,
%U A067277 14,51,9,6,51,26,50,25,30,44,19,49,12,17,24,55,17,47,11,8,43,71,43,16,76
%N A067277 Factorial expansion of zeta(3): zeta(3) = Sum_{n>=1} a(n)/n!.
%H A067277 G. C. Greubel, <a href="/A067277/b067277.txt">Table of n, a(n) for n = 1..10000</a>
%F A067277 a(n) = floor(n!*zeta(3)) - n*floor((n-1)!*zeta(3)), with a(1)=1, for n > 1.
%e A067277 zeta(3) = 1 + 1/3! + 4/5! + 1/6! + 3/7! + 2/8! + 8/9! + 4/10! + ...
%t A067277 With[{b = Zeta[3]}, Table[If[n == 1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]] (* _G. C. Greubel_, Nov 26 2018 *)
%o A067277 (PARI) default(realprecision, 250); b = zeta(3); for(n=1, 80, print1(if(n==1, floor(b), floor(n!*b) - n*floor((n-1)!*b)), ", ")) \\ _G. C. Greubel_, Nov 26 2018
%o A067277 (Magma) SetDefaultRealField(RealField(250)); L:=RiemannZeta(); [Floor(Evaluate(L,3))] cat [Floor(Factorial(n)*Evaluate(L,3)) - n*Floor(Factorial((n-1))*Evaluate(L,3)) : n in [2..80]]; // _G. C. Greubel_, Nov 26 2018
%o A067277 (Sage)
%o A067277 def A067279(n):
%o A067277     if (n==1): return floor(zeta(3))
%o A067277     else: return expand(floor(factorial(n)*zeta(3)) - n*floor(factorial(n-1)*zeta(3)))
%o A067277 [A067279(n) for n in (1..80)] # _G. C. Greubel_, Nov 26 2018
%Y A067277 Cf. A067279 (zeta(2)), A068447 (zeta(4)), A068454 (zeta(5)), A068455 (zeta(6)), A068456 (zeta(7)), A068457 (zeta(8)), A068458 (zeta(9)), A068459 (zeta(10)).
%K A067277 easy,nonn
%O A067277 1,5
%A A067277 _Benoit Cloitre_, Mar 10 2002