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.

A005492 From expansion of falling factorials.

Original entry on oeis.org

4, 15, 52, 151, 372, 799, 1540, 2727, 4516, 7087, 10644, 15415, 21652, 29631, 39652, 52039, 67140, 85327, 106996, 132567, 162484, 197215, 237252, 283111, 335332, 394479, 461140, 535927, 619476, 712447, 815524, 929415, 1054852, 1192591, 1343412, 1508119, 1687540
Offset: 4

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Keywords

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Row n=4 of A108087 (shifted and first term prepended).
Cf. A005490.

Programs

  • Magma
    [n^4 -16*n^3 +102*n^2 -300*n +340: n in [4..50]]; // G. C. Greubel, Dec 01 2022
    
  • Maple
    A005492:=-(15-23*z+41*z**2-13*z**3+4*z**4)/(z-1)**5; # Conjectured by Simon Plouffe in his 1992 dissertation. Gives sequence except for the leading 4.
  • Mathematica
    LinearRecurrence[{5,-10,10,-5,1},{4,15,52,151,372},50] (* Harvey P. Dale, Dec 25 2012 *)
  • SageMath
    [n^4 -16*n^3 +102*n^2 -300*n +340 for n in range(4,51)] # G. C. Greubel, Dec 01 2022

Formula

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
a(n) = n^4 - 16*n^3 + 102*n^2 - 300*n + 340.
G.f.: x^4*(4-5*x+17*x^2+x^3+7*x^4)/(1-x)^5. - Harvey P. Dale, Dec 25 2012
E.g.f.: (1/6)*(-2040 - 762*x - 108*x^2 - 7*x^3 + (2040 - 1278*x + 366*x^2 - 60*x^3 + 6*x^4)*exp(x)). - G. C. Greubel, Dec 01 2022

Extensions

More terms from Pab Ter (pabrlos(AT)yahoo.com), May 09 2004