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.

A143217 a(n) = n! * (!(n+1)) = n! * Sum_{k=0..n} k!.

Original entry on oeis.org

1, 2, 8, 60, 816, 18480, 629280, 29806560, 1864154880, 148459288320, 14652782323200, 1754531527795200, 250496911136102400, 42032247888401971200, 8188505926989625036800, 1832839841629043799552000, 467088574163459753336832000, 134454052266325985991942144000
Offset: 0

Views

Author

Gary W. Adamson, Jul 30 2008

Keywords

Examples

			a(4) = 816 = 4! * 34, where 34 = A003422(4) and A000142 = (1, 1, 2, 6, 24, 120, ...).
a(4) = 816 = sum of row 4 terms of triangle A143216: (24 + 24 + 48 + 144 + 576).

Links

Crossrefs

Cf. A000142, A003422, A061640.
Cf. A143216, A217238, A217239.

Programs

  • Magma
    [Factorial(n)*(&+[Factorial(k): k in [0..n]]): n in [0..30]]; // G. C. Greubel, Jul 12 2022
  • Mathematica
    Table[n!*Sum[i!, {i, 0, n}], {n, 0, 16}]
  • SageMath
    f=factorial; [f(n)*sum(f(k) for k in (0..n)) for n in (0..40)] # G. C. Greubel, Jul 12 2022

Formula

a(n) = A000142(n) * A003422(n+1), where A000142 = the factorials and A003422 = partial sums of the factorials. [Corrected by Georg Fischer, Dec 13 2022]
Equals row sums of triangle A143216.

Extensions

Edited and extended by Olivier Gérard, Sep 28 2012

A217239 a(n) = n!*(!n - 1) = n! * Sum_{k=1..n-1} k!.

Original entry on oeis.org

0, 0, 2, 18, 216, 3960, 110160, 4399920, 238412160, 16777031040, 1484589254400, 161180565638400, 21054377854540800, 3256459838542310400, 588451470350449305600, 122827588903536701184000, 29325437466043778002944000
Offset: 0

Views

Author

Olivier Gérard, Sep 28 2012

Keywords

Comments

Variant of A143217.

Links

Crossrefs

Cf. A000142, A007489, A061640, A217238.

Programs

  • Magma
    [0,0] cat [Factorial(n)*(&+[Factorial(k): k in [1..n-1]]): n in [2..30]]; // G. C. Greubel, Jul 12 2022
  • Mathematica
    Table[n!*Sum[i!, {i, n-1}], {n, 0, 16}]
  • SageMath
    f=factorial; [f(n)*sum(f(k) for k in (1..n-1)) for n in (0..40)] # G. C. Greubel, Jul 12 2022

Formula

a(n) = A000142(n) * A007489(n).
a(n) = n!*(!n - 1) = n! * Sum_{k=1..n-1} k!.
Showing 1-2 of 2 results.

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

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