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.

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A378802 a(n) = n * binomial(4*n, n).

Original entry on oeis.org

0, 4, 56, 660, 7280, 77520, 807576, 8288280, 84146400, 847289520, 8476605280, 84362730452, 836022413616, 8255176274800, 81266247493200, 797911337890800, 7816430993273280, 76417576884236016, 745777615780501920, 7266758081613043600, 70706322844243486400, 687103929058903836480
Offset: 0

Views

Author

Amiram Eldar, Dec 07 2024

Keywords

Crossrefs

Programs

  • Mathematica
    a[n_] := n * Binomial[4*n, n]; Array[a, 25, 0]
  • PARI
    a(n) = n * binomial(4*n, n);

Formula

a(n) = n * A005810(n).
a(n) = A374522(n) + n.
a(n) == 0 (mod 4).
Sum_{n>=1} 1/a(n) = A225847.
Sum_{n>=1} (-1)^n/a(n) = A229703.

A229703 Decimal expansion of Sum_{k>=1} (-1)^k/(k*binomial(4k,k)) (negated).

Original entry on oeis.org

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

Views

Author

R. J. Mathar, Sep 27 2013

Keywords

Examples

			-0.2335324174851719887871681394896038...
		

Crossrefs

Programs

  • Mathematica
    HypergeometricPFQ[{1, 1, 4/3, 5/3}, {5/4, 3/2, 7/4}, -27/256]/4 // RealDigits[#, 10, 105]& // First (* Jean-François Alcover, Feb 18 2014 *)

Formula

Equals (3*d/(2*d^2+1))*log(abs((d-1)/(d+1))) + (3*(d-1)/(2*(2*d^2+1))) * sqrt(d/(d+2)) * arctan(2*sqrt(d^2+2*d)/(d^2+2*d-1)) - (3*(d+1)/(2*(2*d^2+1))) * sqrt(d/(d-2)) * arctan(2*sqrt(d^2-2*d)/(d^2-2*d-1)), where d = sqrt(1 - (8/sqrt(3))*(((3*sqrt(3)+sqrt(283))/16)^(1/3) - (((3*sqrt(3)+sqrt(283))/16)^(-1/3)))) (Batir and Sofo, 2013). - Amiram Eldar, Dec 07 2024
Showing 1-2 of 2 results.