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A068455 Factorial expansion of zeta(6) = Sum_{n>=1} a(n)/n!.

%I A068455 #17 Sep 08 2022 08:45:05
%S A068455 1,0,0,0,2,0,3,3,2,4,5,6,5,9,14,11,3,4,0,15,5,7,10,17,11,14,12,22,4,
%T A068455 17,21,15,26,21,9,3,23,0,4,31,39,21,13,26,16,25,27,13,27,21,19,46,17,
%U A068455 21,25,50,21,44,55,23,20,22,10,49,37,5,55,51,39,40,63,2,6,17,61,52,9,21
%N A068455 Factorial expansion of zeta(6) = Sum_{n>=1} a(n)/n!.
%H A068455 G. C. Greubel, <a href="/A068455/b068455.txt">Table of n, a(n) for n = 1..10000</a>
%t A068455 t = Zeta[6]; s = {}; Do[n = Floor[t*i!]; t -= n/i!; AppendTo[s, n], {i, 1, 30}]; s (* _Amiram Eldar_, Nov 25 2018 *)
%t A068455 With[{b = Zeta[6]}, Table[If[n == 1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]] (* _G. C. Greubel_, Nov 26 2018 *)
%o A068455 (PARI) vector(30,n,if(n>1,t=t%1*n,t=zeta(6))\1) \\ _M. F. Hasler_, Nov 25 2018
%o A068455 (PARI) default(realprecision, 250); for(n=1, 80, print1(if(n==1, floor(zeta(6)), floor(n!*zeta(6)) - n*floor((n-1)!*zeta(6))), ", ")) \\ _G. C. Greubel_, Nov 26 2018
%o A068455 (Magma) SetDefaultRealField(RealField(250)); L:=RiemannZeta(); [Floor(Evaluate(L,6))] cat [Floor(Factorial(n)*Evaluate(L,6)) - n*Floor(Factorial((n-1))*Evaluate(L,6)) : n in [2..80]]; // _G. C. Greubel_, Nov 26 2018
%o A068455 (Sage)
%o A068455 def A068455(n):
%o A068455     if (n==1): return floor(zeta(6))
%o A068455     else: return expand(floor(factorial(n)*zeta(6)) - n*floor(factorial(n-1)*zeta(6)))
%o A068455 [A068455(n) for n in (1..80)] # _G. C. Greubel_, Nov 26 2018
%Y A068455 Cf. A007514.
%K A068455 nonn
%O A068455 1,5
%A A068455 _Benoit Cloitre_, Mar 10 2002
%E A068455 Name edited and keywords cons and easy removed by _M. F. Hasler_, Nov 25 2018