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 1-2 of 2 results.

A282822 a(n) = (n - 4)*n! for n>=0.

Original entry on oeis.org

-4, -3, -4, -6, 0, 120, 1440, 15120, 161280, 1814400, 21772800, 279417600, 3832012800, 56043187200, 871782912000, 14384418048000, 251073478656000, 4623936565248000, 89633231880192000, 1824676506132480000, 38926432130826240000, 868546016919060480000
Offset: 0

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Author

Bruno Berselli, Feb 22 2017

Keywords

Crossrefs

Cf. A034865.
Cf. sequences with formula (n + k)*n! listed in A282466.

Programs

  • Mathematica
    Table[(n - 4) n!, {n, 0, 30}] (* or *)
    RecurrenceTable[{a[0] == -4, a[n] == n a[n - 1] + n!}, a, {n, 0, 30}]

Formula

E.g.f.: -(4 - 5*x)/(1 - x)^2.
a(n) = n*a(n-1) + n!, with n>0, a(0)=-4.
a(n) = 2*A034865(n) for n>3.
From Amiram Eldar, Jan 14 2021: (Start)
Sum_{n>=5} 1/a(n) = 313/288 - 5*e/12 - gamma/24 + Ei(1)/24 = 313/288 - (5/12)*A001113 - (1/24)*A001620 + A091725/24.
Sum_{n>=5} (-1)^(n+1)/a(n) = -25/288 + 1/(6*e) + gamma/24 - Ei(-1)/24 = -25/288 - (1/6)*A068985 + (1/24)*A001620 + (1/24)*A099285. (End)

A034866 a(n) = n!*(n-4)/2, n > 4, and a(4) = 4.

Original entry on oeis.org

4, 60, 720, 7560, 80640, 907200, 10886400, 139708800, 1916006400, 28021593600, 435891456000, 7192209024000, 125536739328000, 2311968282624000, 44816615940096000, 912338253066240000
Offset: 4

Views

Author

Keywords

Programs

  • GAP
    A034866:=Concatenation([4],List([5..20],n->Factorial(n)*(n-4)/2)); # Muniru A Asiru, Feb 17 2018
  • Magma
    [4] cat [Factorial(n)*(n-4)/2: n in [5..30]]; // G. C. Greubel, Feb 16 2018
    
  • Maple
    [4,seq(factorial(n)*(n-4)/2,n=5..20)]; # Muniru A Asiru, Feb 17 2018
  • Mathematica
    Join[{4}, Table[n!*(n-4)/2, {n,5,30}]] (* or *) Drop[With[{nn = 30}, CoefficientList[Series[x^4*(1 + x + x^2)/(6*(1 - x)^2), {x, 0, nn}], x]*Range[0, nn]!], 4]  (* G. C. Greubel, Feb 16 2018 *)
  • PARI
    x='x+O('x^30); Vec(serlaplace(x^4*(1+x+x^2)/(6*(1-x)^2))) \\ G. C. Greubel, Feb 16 2018
    

Formula

a(n) = A034865(n), n > 4. - R. J. Mathar, Oct 20 2008
(-n+5)*a(n) + n*(n-4)*a(n-1) = 0. - R. J. Mathar, Apr 03 2017
E.g.f.: x^4*(1 + x + x^2)/(6*(1 - x)^2). - G. C. Greubel, Feb 16 2018
Showing 1-2 of 2 results.