cp's OEIS Frontend

A068457 Factorial expansion of zeta(8) = Sum_{n>=1} a(n)/n!.

%I A068457 #15 Sep 08 2022 08:45:05
%S A068457 1,0,0,0,0,2,6,4,3,5,10,0,1,11,14,4,2,1,17,12,19,18,18,6,7,24,24,7,9,
%T A068457 14,28,27,14,4,19,33,24,4,14,29,21,38,17,20,5,22,30,7,13,44,19,4,19,
%U A068457 19,14,7,48,9,58,49,17,26,35,33,36,9,28,36,54,36,70,0,33,29,45,14,46,69
%N A068457 Factorial expansion of zeta(8) = Sum_{n>=1} a(n)/n!.
%H A068457 G. C. Greubel, <a href="/A068457/b068457.txt">Table of n, a(n) for n = 1..10000</a>
%t A068457 t = Zeta[8]; s = {}; Do[n = Floor[t*i!]; t -= n/i!; AppendTo[s, n], {i, 1, 30}]; s (* _Amiram Eldar_, Nov 25 2018 *)
%t A068457 With[{b = Zeta[8]}, Table[If[n == 1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]] (* _G. C. Greubel_, Nov 26 2018 *)
%o A068457 (PARI) vector(30,n,if(n>1,t=t%1*n,t=zeta(8))\1) \\ _M. F. Hasler_, Nov 25 2018
%o A068457 (PARI) default(realprecision, 250); for(n=1, 80, print1(if(n==1, floor(zeta(8)), floor(n!*zeta(8)) - n*floor((n-1)!*zeta(8))), ", ")) \\ _G. C. Greubel_, Nov 26 2018
%o A068457 (Magma) SetDefaultRealField(RealField(250)); L:=RiemannZeta(); [Floor(Evaluate(L,8))] cat [Floor(Factorial(n)*Evaluate(L,8)) - n*Floor(Factorial((n-1))*Evaluate(L,8)) : n in [2..80]]; // _G. C. Greubel_, Nov 26 2018
%o A068457 (Sage)
%o A068457 def A068457(n):
%o A068457     if (n==1): return floor(zeta(8))
%o A068457     else: return expand(floor(factorial(n)*zeta(8)) - n*floor(factorial(n-1)*zeta(8)))
%o A068457 [A068457(n) for n in (1..80)] # _G. C. Greubel_, Nov 26 2018
%Y A068457 Cf. A007514, adjacent sequences.
%K A068457 nonn
%O A068457 1,6
%A A068457 _Benoit Cloitre_, Mar 10 2002
%E A068457 Name edited and keywords cons,easy removed by _M. F. Hasler_, Nov 25 2018