A068456 Factorial expansion of zeta(7) = Sum_{n>=1} a(n)/n!.

1, 0, 0, 0, 1, 0, 0, 0, 5, 7, 9, 5, 2, 12, 13, 10, 10, 4, 4, 4, 14, 4, 10, 14, 12, 9, 22, 9, 11, 9, 8, 14, 26, 25, 28, 22, 35, 0, 24, 0, 20, 18, 13, 21, 31, 30, 22, 24, 19, 34, 16, 42, 36, 46, 35, 46, 32, 16, 34, 53, 11, 44, 45, 49, 36, 49, 13, 53, 67, 53, 63, 11, 9, 9, 16, 37, 59, 8

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.

Programs

Magma

SetDefaultRealField(RealField(250)); L:=RiemannZeta(); [Floor(Evaluate(L,7))] cat [Floor(Factorial(n)*Evaluate(L,7)) - n*Floor(Factorial((n-1))*Evaluate(L,7)) : n in [2..80]]; // G. C. Greubel, Nov 26 2018

Mathematica

t = Zeta[7]; s = {}; Do[n = Floor[t*i!]; t -= n/i!; AppendTo[s, n], {i, 1, 30}]; s (* Amiram Eldar, Nov 25 2018 *)
With[{b = Zeta[7]}, 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(7))\1) \\ M. F. Hasler, Nov 25 2018

PARI

default(realprecision, 250); for(n=1, 80, print1(if(n==1, floor(zeta(7)), floor(n!*zeta(7)) - n*floor((n-1)!*zeta(7))), ", ")) \\ G. C. Greubel, Nov 26 2018

Sage

def A068456(n):
    if (n==1): return floor(zeta(7))
    else: return expand(floor(factorial(n)*zeta(7)) - n*floor(factorial(n-1)*zeta(7)))
[A068456(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