A067279 Factorial expansion of zeta(2) : zeta(2) = Sum_{n>=1} a(n)/n!.

1, 1, 0, 3, 2, 2, 2, 3, 6, 6, 8, 1, 11, 12, 7, 6, 13, 7, 3, 2, 2, 2, 9, 20, 9, 16, 11, 0, 12, 13, 19, 25, 26, 31, 18, 24, 21, 32, 12, 34, 22, 24, 13, 14, 41, 20, 34, 29, 22, 40, 50, 4, 33, 50, 39, 8, 15, 24, 14, 59, 40, 3, 9, 29, 27, 14, 18, 39, 59, 44, 28, 30, 35, 5, 64, 20, 18

Offset

1,4

Links

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

Formula

a(n) = floor(n!*zeta(2)) - n*floor((n-1)!*zeta(2)), for n>=2.

Mathematica

With[{b = Zeta[2]}, 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(2); 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, 2))] cat [Floor(Factorial(n)*Evaluate(L, 2)) - n*Floor(Factorial((n-1))*Evaluate(L, 2)) : n in [2..80]]; // G. C. Greubel, Nov 26 2018
(Sage)
def A067279(n):
    if (n==1): return floor(zeta(2))
    else: return expand(floor(factorial(n)*zeta(2)) - n*floor(factorial(n-1)*zeta(2)))
[A067279(n) for n in (1..80)] # G. C. Greubel, Nov 26 2018

Crossrefs

Cf. A067277 (zeta(3)), A068447 (zeta(4)), A068454 (zeta(5)), A068455 (zeta(6)), A068456 (zeta(7)), A068457 (zeta(8)), A068458 (zeta(9)), A068459 (zeta(10)).

Sequence in context: A141070 A283469 A163751 * A106267 A096101 A104890

Adjacent sequences: A067276 A067277 A067278 * A067280 A067281 A067282

Keyword

easy,nonn

Author

Benoit Cloitre, Mar 10 2002

Extensions

a(1) corrected by G. C. Greubel, Nov 26 2018

Status

approved