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 11-16 of 16 results.

A269547 Decimal expansion of Psi(Pi).

Original entry on oeis.org

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

Views

Author

Iaroslav V. Blagouchine, Feb 29 2016

Keywords

Comments

Psi(x) is the digamma function (logarithmic derivative of the Gamma function).

Examples

			0.9772133079420067332920694864061823436408346099943256...

Links

Crossrefs

Cf. A269545, A269546, A269557, A269558, A269559, A257955, A257957, A257958, A257959, A002161.
Cf. A073005, A068466, A175380, A175379, A220086, A203142, A256190, A256191, A256192, A203140, A203139, A203138, A203137.

Programs

  • MATLAB
    format long; psi(pi)
  • Maple
    evalf(Psi(Pi), 120)
  • Mathematica
    RealDigits[PolyGamma[Pi], 10, 120][[1]]
  • PARI
    default(realprecision, 120); psi(Pi)

A269557 Decimal expansion of Gamma(log(2)).

Original entry on oeis.org

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

Views

Author

Iaroslav V. Blagouchine, Feb 29 2016

Keywords

Comments

Gamma(x) is the Gamma function (Euler's integral of the second kind).

Examples

			1.3090409112814812698245325213959295756125890319181890...

Links

Crossrefs

Cf. A269558, A269559, A269545, A269546, A269547, A257955, A257957, A257958, A257959, A002161.
Cf. A073005, A068466, A175380, A175379, A220086, A203142, A256190, A256191, A256192, A203140, A203139, A203138, A203137.

Programs

  • MATLAB
    format long; gamma(log(2))
  • Maple
    evalf(GAMMA(ln(2)), 120);
  • Mathematica
    RealDigits[Gamma[Log[2]], 10, 120][[1]]
  • PARI
    default(realprecision, 120); gamma(log(2))

A269558 Decimal expansion of log(Gamma(log(2))).

Original entry on oeis.org

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

Views

Author

Iaroslav V. Blagouchine, Feb 29 2016

Keywords

Comments

Gamma(x) is the Gamma function (Euler's integral of the second kind).

Examples

			0.2692947402831312429499165832117128248889035102111661...

Links

Crossrefs

Cf. A269557, A269559, A269545, A269546, A269547, A257955, A257957, A257958, A257959, A002161.
Cf. A073005, A068466, A175380, A175379, A220086, A203142, A256190, A256191, A256192, A203140, A203139, A203138, A203137.

Programs

  • MATLAB
    format long; log(gamma(log(2)))
  • Maple
    evalf(lnGAMMA(ln(2)), 120);
  • Mathematica
    RealDigits[LogGamma[Log[2]], 10, 120][[1]]
  • PARI
    default(realprecision, 120); lngamma(log(2))

A269559 Decimal expansion of Psi(log(2)), negated.

Original entry on oeis.org

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

Views

Author

Iaroslav V. Blagouchine, Feb 29 2016

Keywords

Comments

Psi(x) is the digamma function (logarithmic derivative of the Gamma function).

Examples

			-1.2395972796176185082441275516860842454332895226874208...

Links

Crossrefs

Cf. A269557, A269558, A269545, A269546, A269547, A257955, A257957, A257958, A257959, A002161.
Cf. A073005, A068466, A175380, A175379, A220086, A203142, A256190, A256191, A256192, A203140, A203139, A203138, A203137.

Programs

  • MATLAB
    format long; psi(log(2))
  • Maple
    evalf(Psi(ln(2)), 120);
  • Mathematica
    RealDigits[PolyGamma[Log[2]], 10, 120][[1]]
  • PARI
    default(realprecision, 120); psi(log(2))

A034904 Related to sept-factorial numbers A045754.

Original entry on oeis.org

1, 28, 980, 37730, 1531838, 64337196, 2766499428, 121034349975, 5365856182225, 240390356963680, 10861273400995360, 494187939745288880, 22618601857572837200, 1040455685448350511200, 48069052667713793617440, 2229202317465227179008780, 103723472536176158740937940
Offset: 1

Views

Author

Wolfdieter Lang

Keywords

Comments

Convolution of A034835(n-1) with A025752(n), n >= 1.

Links

Crossrefs

Cf. A025752, A034835, A045754, A220086.

Programs

  • Mathematica
    CoefficientList[Series[(Power[1-49x, (-7)^-1]-1)/7,{x,0,30}],x] (* Harvey P. Dale, Aug 23 2011 *)

Formula

a(n) = 7^(n-1)*A045754(n)/n!, where A045754(n) = (7*n-6)(!^7) = Product_{j=1..n} (7*j-6).
G.f.: (-1+(1-49*x)^(-1/7))/7.
D-finite with recurrence: n*a(n) + 7*(-7*n+6)*a(n-1) = 0. - R. J. Mathar, Jan 28 2020
a(n) ~ 7^(2*n-1) * n^(-6/7) / Gamma(1/7). - Amiram Eldar, Aug 18 2025

A371857 Decimal expansion of Integral_{x=0..oo} exp(-x^7) dx.

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, Apr 09 2024

Keywords

Examples

			0.9354375628925463482448704784898566089...

Links

Crossrefs

Decimal expansion of Integral_{x=0..oo} exp(-x^k) dx: A019704 (k=2), A202623 (k=3), A068467 (k=4), A371856 (k=5), A203126 (k=6), this sequence (k=7), A203125 (k=8).
Cf. A220086.

Programs

  • Mathematica
    RealDigits[Gamma[8/7], 10, 106][[1]]

Formula

Equals Gamma(8/7).
Equals A220086 / 7.
Previous Showing 11-16 of 16 results.

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