%I #21 Sep 08 2022 08:45:05
%S 1,0,0,0,0,0,5,0,0,9,1,3,1,0,1,11,2,15,10,18,4,16,9,20,12,6,1,23,20,
%T 14,22,0,8,9,3,26,15,6,13,11,20,32,7,12,31,39,46,36,6,49,7,10,2,5,44,
%U 11,32,41,49,21,40,17,49,62,44,13,25,67,41,57,27,13,24,35,25,43,25,27,29
%N Factorial expansion of zeta(10): zeta(10) = Sum_{n>0} a(n)/n!.
%H G. C. Greubel, <a href="/A068459/b068459.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..150 from Vincenzo Librandi)
%t t = Zeta[10]; s = {}; Do[n = Floor[t*i!]; t -= n/i!; AppendTo[s, n], {i, 1, 30}]; s (* _Amiram Eldar_, Nov 25 2018 *)
%t With[{b = Zeta[10]}, Table[If[n == 1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]] (* _G. C. Greubel_, Nov 26 2018 *)
%o (PARI) vector(30,n,if(n>1,t=t%1*n,t=zeta(10))\1) \\ Increase realprecision (do e.g. \p500) to compute more terms. - _M. F. Hasler_, Nov 25 2018
%o (PARI) default(realprecision, 500); for(n=1, 80, print1(if(n==1, floor(zeta(10)), floor(n!*zeta(10)) - n*floor((n-1)!*zeta(10))), ", ")) \\ _G. C. Greubel_, Nov 26 2018
%o (Magma) SetDefaultRealField(RealField(250)); L:=RiemannZeta(); [Floor(Evaluate(L,10))] cat [Floor(Factorial(n)*Evaluate(L,10)) - n*Floor(Factorial((n-1))*Evaluate(L,10)) : n in [2..80]]; // _G. C. Greubel_, Nov 26 2018
%o (Sage)
%o def A068459(n):
%o if (n==1): return floor(zeta(10))
%o else: return expand(floor(factorial(n)*zeta(10)) - n*floor(factorial(n-1)*zeta(10)))
%o [A068459(n) for n in (1..80)] # _G. C. Greubel_, Nov 26 2018
%Y Cf. A007514.
%K nonn
%O 1,7
%A _Benoit Cloitre_, Mar 10 2002
%E Keywords cons,easy removed by _M. F. Hasler_, Nov 25 2018