A322506 Factorial expansion of 1/exp(2) = Sum_{n>=1} a(n)/n!.

0, 0, 0, 3, 1, 1, 3, 0, 6, 4, 7, 5, 2, 9, 9, 8, 10, 8, 9, 1, 13, 18, 1, 2, 8, 15, 26, 10, 22, 1, 18, 9, 20, 10, 2, 6, 13, 19, 16, 38, 38, 3, 32, 5, 39, 24, 7, 27, 14, 41, 20, 39, 32, 7, 20, 35, 44, 50, 24, 34, 51, 14, 39, 47, 49, 15, 61, 54, 60, 52, 34, 60, 32, 72, 48, 12, 67, 52, 22, 48

Offset

1,4

Links

Table of n, a(n) for n=1..80.

Index entries for factorial base representation

Example

1/exp(2) = 0 + 0/2! + 0/3! + 3/4! + 1/5! + 1/6! + 3/7! + 0/8! + 6/9! +...

Mathematica

With[{b = 1/E^2}, Table[If[n == 1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]]

Prog

(PARI) default(realprecision, 250); b = exp(-2); for(n=1, 80, print1(if(n==1, floor(b), floor(n!*b) - n*floor((n-1)!*b)), ", "))
(Magma) SetDefaultRealField(RealField(250));  [Floor(Exp(-2))] cat [Floor(Factorial(n)*Exp(-2)) - n*Floor(Factorial((n-1))*Exp(-2)) : n in [2..80]];
(Sage)
b=exp(-2);
def a(n):
    if (n==1): return floor(b)
    else: return expand(floor(factorial(n)*b) -n*floor(factorial(n-1)*b))
[a(n) for n in (1..80)]

Crossrefs

Cf. A092553 (decimal expansion), 0 U A001204 (continued fraction).

Cf. A054977 (e), A067840 (e^2), A068453 (sqrt(e)), A237420 (1/e).

Sequence in context: A104443 A218489 A218332 * A103496 A345441 A267863

Adjacent sequences: A322503 A322504 A322505 * A322507 A322508 A322509

Keyword

nonn

Author

G. C. Greubel, Dec 12 2018

Status

approved