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 1-3 of 3 results.

A371745 Decimal expansion of Sum_{k>=0} (-1)^k * k / ((k+1) (2k)!).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, May 01 2024

Keywords

Examples

			-0.2232442754839327307059412507035746029774...

Crossrefs

Cf. A372339, A372340.

Programs

  • Mathematica
    s = Sum[(-1)^k k/((k + 1) (2 k)!), {k, 0, Infinity}]
d = N[s, 100]
First[RealDigits[d]]

Formula

Equals 2 - cos(1) - 2 sin(1).

A372338 Decimal expansion of Sum_{k>=0} (k+2) / ((k+1)*(2k)!).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Apr 28 2024

Keywords

Examples

			2.8073217524723591352868580804341...

Crossrefs

Cf. A073742, A073743, A372339.

Programs

  • Mathematica
    s = Sum[(k + 2)/((k + 1) (2 k)!), {k, 0, Infinity}]
d = N[s, 100]
First[RealDigits[d]]

Formula

Equals -4/e + 2 + 3*cosh(1) - 2*sinh(1).
Equals 2*2F3(1,3; 1/2,2,2; 1/4). - R. J. Mathar, Aug 02 2024

A372340 Decimal expansion of Sum_{k>=0} k /((k+1)*(2k)!).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, May 01 2024

Keywords

Examples

			0.278839517158128421668953161079983417493...

Crossrefs

Cf. A371745, A372339.

Programs

  • Mathematica
    s = Sum[k/((k + 1) (2 k)!), {k, 0, Infinity}]
d = N[s, 100]
First[RealDigits[d]]

Formula

Equals -2 + 3 cosh(1) - 2 sinh(1).
Equals 1F2(2; 3/2,3; 1/4)/4. - R. J. Mathar, Aug 02 2024
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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