A068459 Factorial expansion of zeta(10): zeta(10) = Sum_{n>0} a(n)/n!.

1, 0, 0, 0, 0, 0, 5, 0, 0, 9, 1, 3, 1, 0, 1, 11, 2, 15, 10, 18, 4, 16, 9, 20, 12, 6, 1, 23, 20, 14, 22, 0, 8, 9, 3, 26, 15, 6, 13, 11, 20, 32, 7, 12, 31, 39, 46, 36, 6, 49, 7, 10, 2, 5, 44, 11, 32, 41, 49, 21, 40, 17, 49, 62, 44, 13, 25, 67, 41, 57, 27, 13, 24, 35, 25, 43, 25, 27, 29

Offset: 1

Author

Benoit Cloitre, Mar 10 2002

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000 (terms 1..150 from Vincenzo Librandi)

Crossrefs

Cf. A007514.

Programs

Magma

SetDefaultRealField(RealField(250)); L:=RiemannZeta(); [Floor(Evaluate(L,10))] cat [Floor(Factorial(n)*Evaluate(L,10)) - n*Floor(Factorial((n-1))*Evaluate(L,10)) : n in [2..80]]; // G. C. Greubel, Nov 26 2018

Mathematica

t = Zeta[10]; s = {}; Do[n = Floor[t*i!]; t -= n/i!; AppendTo[s, n], {i, 1, 30}]; s (* Amiram Eldar, Nov 25 2018 *)
With[{b = Zeta[10]}, 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(10))\1) \\ Increase realprecision (do e.g. \p500) to compute more terms. - M. F. Hasler, Nov 25 2018

PARI

default(realprecision, 500); for(n=1, 80, print1(if(n==1, floor(zeta(10)), floor(n!*zeta(10)) - n*floor((n-1)!*zeta(10))), ", ")) \\ G. C. Greubel, Nov 26 2018

Sage

def A068459(n):
    if (n==1): return floor(zeta(10))
    else: return expand(floor(factorial(n)*zeta(10)) - n*floor(factorial(n-1)*zeta(10)))
[A068459(n) for n in (1..80)] # G. C. Greubel, Nov 26 2018

Extensions

Keywords cons,easy removed by M. F. Hasler, Nov 25 2018