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Factorial expansion: zeta(4) = Pi^4/90 = Sum_{n>0} a(n)/n!.
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%I #28 Sep 08 2022 08:45:05

%S 1,0,0,1,4,5,1,7,2,4,6,0,8,8,14,14,14,12,0,14,2,5,15,9,11,25,12,9,1,

%T 21,29,29,20,22,29,21,27,10,4,13,20,20,30,11,7,18,18,15,39,8,47,41,51,

%U 36,28,50,35,32,6,38,23,41,45,49,36,11,31,60,5,50,42,61,1,61,68,43,76,41

%N Factorial expansion: zeta(4) = Pi^4/90 = Sum_{n>0} a(n)/n!.

%H G. C. Greubel, <a href="/A068447/b068447.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Factorial_number_system#Fractional_values">Factorial number system: Fractional values</a>.

%H <a href="/index/Fa#facbase">Index to sequences related to factorial base representation of noninteger constants</a>.

%t Table[If[n == 1, Floor[Pi^4/90], Floor[n!*(Pi^4/90)] - n*Floor[(n- 1)!*(Pi^4/90)]], {n, 1, 50}] (* _G. C. Greubel_, Mar 21 2018 *)

%o (PARI) for(n=1,30, print1(if(n==1, floor(Pi^4/90), floor(n!*Pi^4/90) - n*floor((n-1)!*Pi^4/90)), ", ")) \\ _G. C. Greubel_, Mar 21 2018

%o (PARI) A068447_vec(N=90,c=zeta(precision(4.,N*log(N/2.4)\/2.3)))=vector(N,n,if(n>1,c=c%1*n,c)\1) \\ _M. F. Hasler_, Nov 28 2018

%o (Magma) R:= RealField(200); [Floor(Pi(R)^4/90)] cat [Floor(Factorial(n)* Pi(R)^4/90) - n*Floor(Factorial((n-1))*Pi(R)^4/90) : n in [2..78]]; // _G. C. Greubel_, Mar 21 2018

%Y Cf. A013662 (decimal expansion).

%K easy,nonn

%O 1,5

%A _Benoit Cloitre_, Mar 10 2002