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A068455
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Factorial expansion of zeta(6) = Sum_{n>=1} a(n)/n!.
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4
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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, 17, 21, 15, 26, 21, 9, 3, 23, 0, 4, 31, 39, 21, 13, 26, 16, 25, 27, 13, 27, 21, 19, 46, 17, 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
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OFFSET
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1,5
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LINKS
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MATHEMATICA
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t = Zeta[6]; s = {}; Do[n = Floor[t*i!]; t -= n/i!; AppendTo[s, n], {i, 1, 30}]; s (* Amiram Eldar, Nov 25 2018 *)
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 *)
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PROG
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(PARI) vector(30, n, if(n>1, t=t%1*n, t=zeta(6))\1) \\ M. F. Hasler, Nov 25 2018
(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
(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
(Sage)
if (n==1): return floor(zeta(6))
else: return expand(floor(factorial(n)*zeta(6)) - n*floor(factorial(n-1)*zeta(6)))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Name edited and keywords cons and easy removed by M. F. Hasler, Nov 25 2018
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STATUS
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approved
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