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

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, 14, 28, 27, 14, 4, 19, 33, 24, 4, 14, 29, 21, 38, 17, 20, 5, 22, 30, 7, 13, 44, 19, 4, 19, 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

Offset: 1

Author

Benoit Cloitre, Mar 10 2002

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007514, adjacent sequences.

Programs

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

Mathematica

t = Zeta[8]; s = {}; Do[n = Floor[t*i!]; t -= n/i!; AppendTo[s, n], {i, 1, 30}]; s (* Amiram Eldar, Nov 25 2018 *)
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 *)

PARI

vector(30,n,if(n>1,t=t%1*n,t=zeta(8))\1) \\ M. F. Hasler, Nov 25 2018

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

Sage

def A068457(n):
    if (n==1): return floor(zeta(8))
    else: return expand(floor(factorial(n)*zeta(8)) - n*floor(factorial(n-1)*zeta(8)))
[A068457(n) for n in (1..80)] # G. C. Greubel, Nov 26 2018

Extensions

Name edited and keywords cons,easy removed by M. F. Hasler, Nov 25 2018