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 1-3 of 3 results.

A064319 Triangle with a(n,1) = n and a(n,k) = a(n,k-1) * a(n-1,k-1).

Original entry on oeis.org

1, 2, 2, 3, 6, 12, 4, 12, 72, 864, 5, 20, 240, 17280, 14929920, 6, 30, 600, 144000, 2488320000, 37150418534400000, 7, 42, 1260, 756000, 108864000000, 270888468480000000000, 10063619980174622195712000000000000000, 8, 56
Offset: 1

Views

Author

Henry Bottomley, Sep 10 2001

Keywords

Examples

			Rows start
  1;
  2,  2;
  3,  6, 12;
  4, 12, 72, 864;
  ...

Crossrefs

Columns include A000027, A002378, A047928, A064321. Right-hand side is A064320. Cf. A053218 which uses addition rather than multiplication to produce binomial transform.

Extensions

Name corrected by Sean A. Irvine, Jun 30 2023

A064321 a(n) = n*(n-1)^3*(n-2)^3*(n-3).

Original entry on oeis.org

0, 0, 0, 0, 864, 17280, 144000, 756000, 2963520, 9483264, 26127360, 64152000, 143748000, 298995840, 584648064, 1085142240, 1926288000, 3290112000, 5433384960, 8710395264, 13600573920, 20741616000, 30968784000, 45361118880, 65295324864, 92508134400, 129168000000
Offset: 0

Views

Author

Henry Bottomley, Sep 10 2001

Keywords

Examples

			a(4) = 4*(3^3)*(2^3)*1 = 4*27*8*1 = 864.

Links

Crossrefs

Cf. A000027, A002378, A047928, A064319, A064320.

Programs

  • Maple
    A064321:=n->n*(n-1)^3*(n-2)^3*(n-3); seq(A064321(n), n=0..50); # Wesley Ivan Hurt, Feb 02 2014
  • Mathematica
    Table[n (n - 3) (n - 1)^3*(n - 2)^3, {n, 0, 50}] (* Wesley Ivan Hurt, Feb 02 2014 *)
  • PARI
    a(n) = { n*(n - 1)^3*(n - 2)^3*(n - 3) } \\ Harry J. Smith, Sep 11 2009
  • PARI
    concat([0,0,0,0], Vec(-288*x^4*(3*x^4+33*x^3+68*x^2+33*x+3)/(x-1)^9 + O(x^100))) \\ Colin Barker, Sep 14 2014

Formula

G.f.: -288*x^4*(3*x^4+33*x^3+68*x^2+33*x+3) / (x-1)^9. - Colin Barker, Sep 14 2014

A085916 Array T(i,1)=i, T(1,j)=j and T(i,j)=T(i-1,j-1)*T(i,j-1) read by antidiagonals.

Original entry on oeis.org

1, 2, 2, 3, 2, 3, 4, 4, 6, 4, 5, 12, 12, 12, 5, 6, 48, 48, 72, 20, 6, 7, 240, 576, 864, 240, 30, 7, 8, 1440, 27648, 41472, 17280, 600, 42, 8, 9, 10080, 6635520, 23887872, 14929920, 144000, 1260, 56, 9, 10, 80640, 9555148800, 660451885056, 619173642240
Offset: 1

Views

Author

Benoit Cloitre, Aug 16 2003

Keywords

Crossrefs

Cf. A064320 (main diagonal).

Extensions

Definition corrected by Georg Fischer, Jan 31 2022
Showing 1-3 of 3 results.

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

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