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Factorial expansion of zeta(9) = Sum_{n>=1} a(n)/n!.
4

%I #15 Sep 08 2022 08:45:05

%S 1,0,0,0,0,1,3,0,8,8,0,7,4,12,9,8,11,11,9,16,15,11,10,11,1,16,13,25,

%T 24,0,15,23,12,32,18,21,20,15,20,19,18,1,5,18,20,13,16,35,6,46,40,28,

%U 9,3,19,34,14,6,0,26,48,45,58,10,0,36,32,21,30,42,12,65,54,26,29,15,46,65

%N Factorial expansion of zeta(9) = Sum_{n>=1} a(n)/n!.

%H G. C. Greubel, <a href="/A068458/b068458.txt">Table of n, a(n) for n = 1..2500</a>

%t t = Zeta[9]; 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[9]}, 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(9))\1) \\ _M. F. Hasler_, Nov 25 2018

%o (PARI) default(realprecision, 250); for(n=1, 80, print1(if(n==1, floor(zeta(9)), floor(n!*zeta(9)) - n*floor((n-1)!*zeta(9))), ", ")) \\ _G. C. Greubel_, Nov 26 2018

%o (Magma) SetDefaultRealField(RealField(250)); L:=RiemannZeta(); [Floor(Evaluate(L,9))] cat [Floor(Factorial(n)*Evaluate(L,9)) - n*Floor(Factorial((n-1))*Evaluate(L,9)) : n in [2..80]]; // _G. C. Greubel_, Nov 26 2018

%o (Sage)

%o def A068458(n):

%o if (n==1): return floor(zeta(9))

%o else: return expand(floor(factorial(n)*zeta(9)) - n*floor(factorial(n-1)*zeta(9)))

%o [A068458(n) for n in (1..80)] # _G. C. Greubel_, Nov 26 2018

%Y Cf. A007514, adjacent sequences.

%K nonn

%O 1,7

%A _Benoit Cloitre_, Mar 10 2002