A068447 Factorial expansion: zeta(4) = Pi^4/90 = Sum_{n>0} a(n)/n!.

1, 0, 0, 1, 4, 5, 1, 7, 2, 4, 6, 0, 8, 8, 14, 14, 14, 12, 0, 14, 2, 5, 15, 9, 11, 25, 12, 9, 1, 21, 29, 29, 20, 22, 29, 21, 27, 10, 4, 13, 20, 20, 30, 11, 7, 18, 18, 15, 39, 8, 47, 41, 51, 36, 28, 50, 35, 32, 6, 38, 23, 41, 45, 49, 36, 11, 31, 60, 5, 50, 42, 61, 1, 61, 68, 43, 76, 41

Offset: 1

Author

Benoit Cloitre, Mar 10 2002

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Wikipedia, Factorial number system: Fractional values.
• Index to sequences related to factorial base representation of noninteger constants.

Crossrefs

Cf. A013662 (decimal expansion).

Programs

Magma

R:= RealField(200); [Floor(Pi(R)^4/90)] cat [Floor(Factorial(n)* Pi(R)^4/90) - n*Floor(Factorial((n-1))*Pi(R)^4/90) : n in [2..78]]; // G. C. Greubel, Mar 21 2018

Mathematica

Table[If[n == 1, Floor[Pi^4/90], Floor[n!*(Pi^4/90)] - n*Floor[(n- 1)!*(Pi^4/90)]], {n, 1, 50}] (* G. C. Greubel, Mar 21 2018 *)

PARI

for(n=1,30, print1(if(n==1, floor(Pi^4/90), floor(n!*Pi^4/90) - n*floor((n-1)!*Pi^4/90)), ", ")) \\ G. C. Greubel, Mar 21 2018

PARI

A068447_vec(N=90,c=zeta(precision(4.,N*log(N/2.4)\/2.3)))=vector(N,n,if(n>1,c=c%1*n,c)\1) \\ M. F. Hasler, Nov 28 2018