A068453 Factorial expansion of sqrt(e) = Sum_{n>=1} a(n)/n!.

1, 1, 0, 3, 2, 5, 0, 4, 3, 9, 8, 2, 8, 0, 10, 15, 2, 10, 8, 19, 12, 4, 18, 23, 8, 4, 21, 15, 17, 1, 11, 19, 7, 25, 15, 3, 20, 5, 24, 25, 35, 9, 12, 25, 26, 22, 23, 11, 43, 46, 6, 0, 25, 27, 30, 6, 14, 20, 33, 5, 30, 23, 42, 4, 11, 19, 55, 63, 43, 12, 52, 51, 22, 29, 11, 8, 19, 35, 25

Offset: 1

Author

Benoit Cloitre, Mar 10 2002

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A067840 (e^2), A075874 (Pi).

Programs

Magma

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

Mathematica

With[{b = Sqrt[E]}, 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=exp(.5))\1) \\ M. F. Hasler, Nov 25 2018

PARI

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

Sage

def A068453(n):
    if (n==1): return floor(sqrt(e))
    else: return expand(floor(factorial(n)*sqrt(e)) - n*floor(factorial(n-1)*sqrt(e)))
[A068453(n) for n in (1..80)] # G. C. Greubel, Nov 26 2018

Extensions

Name edited and keyword cons removed by M. F. Hasler, Nov 25 2018