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 1-4 of 4 results.

A248676 Decimal expansion of r = sum_{n >= 0} floor(n/3)!/n!.

Original entry on oeis.org

2, 7, 1, 9, 9, 0, 9, 2, 6, 5, 4, 9, 0, 8, 5, 3, 8, 3, 4, 2, 1, 3, 2, 2, 2, 8, 6, 5, 2, 2, 4, 5, 2, 5, 2, 1, 1, 9, 3, 3, 1, 0, 0, 7, 6, 0, 4, 8, 4, 7, 1, 6, 7, 2, 7, 5, 0, 8, 5, 8, 8, 5, 5, 8, 9, 5, 9, 7, 4, 1, 7, 4, 6, 6, 1, 0, 2, 9, 5, 5, 8, 4, 9, 5, 0, 1
Offset: 1

Views

Author

Clark Kimberling, Oct 11 2014

Keywords

Examples

			r = 2.71990926549085383421322286522452521...

Links

Crossrefs

Cf. A248675, A248677, A248664.

Programs

  • Maple
    evalf(sum(floor(n/3)!/n!, n=0..infinity),120); # Vaclav Kotesovec, Oct 17 2014
  • Mathematica
    x = N[Sum[Floor[n/2]!/n!, {n, 0, 200}], 120]
RealDigits[x][[1]]  (* A248675 *)
x = N[Sum[Floor[n/3]!/n!, {n, 0, 200}], 120]
RealDigits[x][[1]]  (* A248676 *)
x = N[Sum[Floor[n/4]!/n!, {n, 0, 200}], 120]
RealDigits[x][[1]]  (* A248677 *)

Formula

r = sum_{n >= 0} p(3,n)*n!/(3*n + 2)!, where p(k,n) is defined at A248664.

A248677 Decimal expansion of r = sum_{n >= 0} floor(n/4)!/n!.

Original entry on oeis.org

2, 7, 1, 8, 3, 0, 9, 6, 9, 7, 7, 0, 7, 2, 4, 5, 6, 1, 8, 3, 3, 0, 4, 0, 8, 2, 7, 6, 3, 6, 1, 8, 7, 3, 4, 7, 9, 6, 2, 8, 7, 6, 1, 1, 1, 3, 3, 9, 4, 8, 9, 6, 3, 4, 3, 2, 0, 6, 4, 4, 2, 4, 2, 6, 1, 7, 4, 1, 3, 1, 3, 5, 4, 3, 9, 1, 2, 8, 2, 4, 3, 8, 1, 9, 6, 1
Offset: 1

Views

Author

Clark Kimberling, Oct 11 2014

Keywords

Examples

			r = 2.718309697707245618330408276361873...

Links

Crossrefs

Cf. A248675, A248676, A248664.

Programs

  • Maple
    evalf(sum(floor(n/4)!/n!, n=0..infinity),120); # Vaclav Kotesovec, Oct 17 2014
  • Mathematica
    x = N[Sum[Floor[n/2]!/n!, {n, 0, 200}], 120]
RealDigits[x][[1]]  (* A248675 *)
x = N[Sum[Floor[n/3]!/n!, {n, 0, 200}], 120]
RealDigits[x][[1]]  (* A248676 *)
x = N[Sum[Floor[n/4]!/n!, {n, 0, 200}], 120]
RealDigits[x][[1]]  (* A248677 *)

Formula

r = sum_{n >= 0} p(4,n)*n!/(4*n + 3)!, where p(k,n) is defined at A248664.

A248678 Decimal expansion of r = sum_{n >= 0} floor(2n/3)!/n!.

Original entry on oeis.org

3, 0, 1, 0, 1, 4, 4, 8, 5, 3, 9, 9, 1, 0, 5, 2, 3, 2, 1, 9, 1, 1, 6, 4, 6, 1, 4, 8, 7, 6, 7, 7, 3, 2, 7, 6, 3, 9, 3, 1, 8, 3, 7, 7, 0, 2, 6, 1, 7, 5, 6, 1, 1, 0, 7, 9, 9, 7, 1, 8, 8, 1, 1, 9, 5, 6, 5, 8, 4, 9, 3, 9, 2, 1, 4, 0, 5, 0, 9, 3, 5, 7, 5, 6, 7, 9
Offset: 1

Views

Author

Clark Kimberling, Oct 11 2014

Keywords

Examples

			r = 3.0101448539910523219116461487677327...

Links

Crossrefs

Cf. A248675, A248676, A248677.

Programs

  • Maple
    evalf(sum(floor(2n/3)!/n!, n=0..infinity),120); # Vaclav Kotesovec, Oct 17 2014
  • Mathematica
    x = N[Sum[Floor[2 n/3]!/n!, {n, 0, 200}], 120]
RealDigits[x][[1]]  (* A248678 *)

Formula

r = sum_{n >= 0} (9 n^2 + 14 n + 5) (2 n)!/(3 n + 2)!.

A371941 Decimal expansion of Sum_{k>=0} (k+1)! / (2*k+1)!.

Original entry on oeis.org

1, 3, 8, 8, 4, 4, 4, 8, 0, 4, 7, 0, 3, 9, 8, 9, 8, 6, 3, 4, 9, 0, 6, 2, 2, 5, 8, 1, 8, 0, 8, 5, 9, 4, 0, 3, 0, 9, 2, 6, 9, 2, 4, 9, 1, 8, 3, 2, 5, 4, 8, 0, 6, 5, 5, 6, 6, 3, 5, 2, 8, 7, 5, 4, 7, 9, 8, 0, 5, 5, 1, 9, 4, 2, 4, 9, 7, 6, 1, 3, 3, 5, 5, 4, 0, 8
Offset: 1

Views

Author

Clark Kimberling, Apr 28 2024

Keywords

Examples

			1.38844480470398986349062258180859403...

Crossrefs

Cf. A248675, A371946.

Programs

  • Maple
    hypergeom([2], [3/2], 1/4) ; evalf(%) ; # R. J. Mathar, Jul 03 2024
  • Mathematica
    s = Sum[(k + 1)!/(2 k+1)!, {k, 0, Infinity}]
d = N[s, 100]
First[RealDigits[d]]

Formula

Equals (1/4)*(2 + e^(1/4)*sqrt(Pi)*erf(1/2)).
Equals A248675/2. - Hugo Pfoertner, Apr 29 2024
Showing 1-4 of 4 results.

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