A067277 Factorial expansion of zeta(3): zeta(3) = Sum_{n>=1} a(n)/n!.

1, 0, 1, 0, 4, 1, 3, 2, 8, 4, 0, 11, 11, 10, 9, 4, 2, 11, 5, 12, 16, 12, 6, 3, 22, 22, 12, 14, 23, 1, 24, 24, 12, 14, 1, 27, 14, 26, 21, 16, 22, 14, 6, 19, 12, 12, 36, 22, 32, 38, 10, 1, 14, 51, 9, 6, 51, 26, 50, 25, 30, 44, 19, 49, 12, 17, 24, 55, 17, 47, 11, 8, 43, 71, 43, 16, 76

Offset

1,5

Links

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

Formula

a(n) = floor(n!*zeta(3)) - n*floor((n-1)!*zeta(3)), with a(1)=1, for n > 1.

Example

zeta(3) = 1 + 1/3! + 4/5! + 1/6! + 3/7! + 2/8! + 8/9! + 4/10! + ...

Mathematica

With[{b = Zeta[3]}, Table[If[n == 1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]] (* G. C. Greubel, Nov 26 2018 *)

Prog

(PARI) default(realprecision, 250); b = zeta(3); for(n=1, 80, print1(if(n==1, floor(b), floor(n!*b) - n*floor((n-1)!*b)), ", ")) \\ G. C. Greubel, Nov 26 2018
(Magma) SetDefaultRealField(RealField(250)); L:=RiemannZeta(); [Floor(Evaluate(L, 3))] cat [Floor(Factorial(n)*Evaluate(L, 3)) - n*Floor(Factorial((n-1))*Evaluate(L, 3)) : n in [2..80]]; // G. C. Greubel, Nov 26 2018
(Sage)
def A067279(n):
    if (n==1): return floor(zeta(3))
    else: return expand(floor(factorial(n)*zeta(3)) - n*floor(factorial(n-1)*zeta(3)))
[A067279(n) for n in (1..80)] # G. C. Greubel, Nov 26 2018

Crossrefs

Cf. A067279 (zeta(2)), A068447 (zeta(4)), A068454 (zeta(5)), A068455 (zeta(6)), A068456 (zeta(7)), A068457 (zeta(8)), A068458 (zeta(9)), A068459 (zeta(10)).

Sequence in context: A344439 A342403 A019633 * A177951 A222130 A061903

Adjacent sequences: A067274 A067275 A067276 * A067278 A067279 A067280

Keyword

easy,nonn

Author

Benoit Cloitre, Mar 10 2002

Status

approved