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.

Previous Showing 11-14 of 14 results.

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.

A248683 Decimal expansion of r = sum{(floor(n/3)!)^3/n!, n >= 0}.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 11 2014

Keywords

Examples

			r = 2.7302563769633613858049832744771976271...

Links

Crossrefs

Cf. A248682, A248684, A248685, A248664.

Programs

  • Mathematica
    RealDigits[Sum[(Floor[n/3])!^3/n!, {n, 0, 400}], 10, 111][[1]]
  • PARI
    suminf(n=0, ((n\3)!)^3/n!) \\ Michel Marcus, Feb 23 2016

Formula

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

A248684 Decimal expansion of r = sum{(floor(n/4)!)^4/n!, n >= 0}.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 11 2014

Keywords

Examples

			r = 2.718702641910851497086752200287756621...

Links

Crossrefs

Cf. A248682, A248683, A248685, A248664.

Programs

  • Mathematica
    RealDigits[Sum[(Floor[n/4])!^4/n!, {n, 0, 400}], 10, 111][[1]]
  • PARI
    suminf(n=0, ((n\4)!)^4/n!) \\ Michel Marcus, Feb 23 2016

Formula

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

A248685 Decimal expansion of r = sum{(floor(n/5)!)^5/n!, n >= 0}.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 11 2014

Keywords

Examples

			r = 2.71829122423905735499923669685865...

Links

Crossrefs

Cf. A248682, A248683, A248684, A248664.

Programs

  • Mathematica
    x = N[Sum[(Floor[n/2])!^2/n!, {n, 0, 200}], 120]
RealDigits[x][[1]]  (* A248682 *)
x = N[Sum[(Floor[n/3])!^3/n!, {n, 0, 200}], 120]
RealDigits[x][[1]]  (* A248683 *)
x = N[Sum[(Floor[n/4])!^4/n!, {n, 0, 200}], 120]
RealDigits[x][[1]]  (* A248684 *)
x = N[Sum[(Floor[n/5])!^5/n!, {n, 0, 200}], 120]
RealDigits[x][[1]]  (* A248685 *)

Formula

r = sum{(n!^5)*p(5,n)/(5*n + 4)!, n >= 0}, where p(k,n) is defined at A248664.
Previous Showing 11-14 of 14 results.

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