cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A030799 a(n) = floor(exp(1/2)*n!).

Original entry on oeis.org

1, 3, 9, 39, 197, 1187, 8309, 66476, 598287, 5982879, 65811677, 789740126, 10266621646, 143732703044, 2155990545670, 34495848730735, 586429428422497, 10555729711604956, 200558864520494172, 4011177290409883459
Offset: 1

Views

Author

Simon Plouffe

Keywords

Links

Crossrefs

Cf. A068453.

Programs

  • Maple
    f:= n -> floor(exp(1/2)*n!):
map(f, [$1..30]); # Robert Israel, Oct 16 2019
  • Mathematica
    Floor[Exp[1/2]Range[20]!] (* Harvey P. Dale, Aug 19 2020 *)

Formula

a(n+1) = (n+1)*a(n) + A068453(n+1). - Robert Israel, Oct 16 2019

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

Original entry on oeis.org

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

Views

Author

G. C. Greubel, Dec 12 2018

Keywords

Examples

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

Links

Crossrefs

Cf. A092553 (decimal expansion), 0 U A001204 (continued fraction).
Cf. A054977 (e), A067840 (e^2), A068453 (sqrt(e)), A237420 (1/e).

Programs

  • Magma
    SetDefaultRealField(RealField(250));  [Floor(Exp(-2))] cat [Floor(Factorial(n)*Exp(-2)) - n*Floor(Factorial((n-1))*Exp(-2)) : n in [2..80]];
  • Mathematica
    With[{b = 1/E^2}, Table[If[n == 1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]]
  • 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)), ", "))
  • 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)]
Showing 1-2 of 2 results.

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