A068458 Factorial expansion of zeta(9) = Sum_{n>=1} a(n)/n!.

1, 0, 0, 0, 0, 1, 3, 0, 8, 8, 0, 7, 4, 12, 9, 8, 11, 11, 9, 16, 15, 11, 10, 11, 1, 16, 13, 25, 24, 0, 15, 23, 12, 32, 18, 21, 20, 15, 20, 19, 18, 1, 5, 18, 20, 13, 16, 35, 6, 46, 40, 28, 9, 3, 19, 34, 14, 6, 0, 26, 48, 45, 58, 10, 0, 36, 32, 21, 30, 42, 12, 65, 54, 26, 29, 15, 46, 65

Offset: 1

Author

Benoit Cloitre, Mar 10 2002

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..2500

Crossrefs

Cf. A007514, adjacent sequences.

Programs

Magma

SetDefaultRealField(RealField(250)); L:=RiemannZeta(); [Floor(Evaluate(L,9))] cat [Floor(Factorial(n)*Evaluate(L,9)) - n*Floor(Factorial((n-1))*Evaluate(L,9)) : n in [2..80]]; // G. C. Greubel, Nov 26 2018

Mathematica

t = Zeta[9]; s = {}; Do[n = Floor[t*i!]; t -= n/i!; AppendTo[s, n], {i, 1, 30}]; s (* Amiram Eldar, Nov 25 2018 *)
With[{b = Zeta[9]}, 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(9))\1) \\ M. F. Hasler, Nov 25 2018

PARI

default(realprecision, 250); for(n=1, 80, print1(if(n==1, floor(zeta(9)), floor(n!*zeta(9)) - n*floor((n-1)!*zeta(9))), ", ")) \\ G. C. Greubel, Nov 26 2018

Sage

def A068458(n):
    if (n==1): return floor(zeta(9))
    else: return expand(floor(factorial(n)*zeta(9)) - n*floor(factorial(n-1)*zeta(9)))
[A068458(n) for n in (1..80)] # G. C. Greubel, Nov 26 2018