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.

A082039 Symmetric square array defined by T(n,k) = k^2*n^2 + k*n + 1, read by antidiagonals.

Original entry on oeis.org

1, 1, 1, 1, 3, 1, 1, 7, 7, 1, 1, 13, 21, 13, 1, 1, 21, 43, 43, 21, 1, 1, 31, 73, 91, 73, 31, 1, 1, 43, 111, 157, 157, 111, 43, 1, 1, 57, 157, 241, 273, 241, 157, 57, 1, 1, 73, 211, 343, 421, 421, 343, 211, 73, 1, 1, 91, 273, 463, 601, 651, 601, 463, 273, 91, 1, 1, 111, 343, 601, 813, 931, 931, 813, 601, 343, 111, 1
Offset: 0

Views

Author

Paul Barry, Apr 02 2003

Keywords

Examples

			Square array T(n,k) begins:
  1  1  1   1   1   1 ...
  1  3  7  13  21  31 ...
  1  7 21  43  73 111 ...
  1 13 43  91 157 241 ...
  1 21 73 157 273 421 ...
  ...

Crossrefs

Rows include A054569, A002061, A082040, A082041.
Main diagonal is A059826.
Cf. A082038.

A082035 a(n) = (4n^2+2n+1) * n!.

Original entry on oeis.org

1, 7, 42, 258, 1752, 13320, 113040, 1063440, 11007360, 124467840, 1527724800, 20237817600, 287879961600, 4377595622400, 70875950745600, 1217444836608000, 22115388911616000, 423623726862336000, 8534364149735424000
Offset: 0

Views

Author

Paul Barry, Apr 02 2003

Keywords

Comments

A row of the number array A082038.

Crossrefs

Cf. A001564, A082036.

Programs

  • Mathematica
    Table[(4n^2+2n+1)n!,{n,0,20}] (* Harvey P. Dale, Jul 15 2011 *)

Formula

a(n) = 4*A002775(n) + A007680(n).

A082036 a(n) = (9*n^2+3*n+1) * n!.

Original entry on oeis.org

1, 13, 86, 546, 3768, 28920, 246960, 2333520, 24232320, 274700160, 3378412800, 44826566400, 638509132800, 9720379468800, 157531172198400, 2708193616128000, 49231324606464000, 943638746738688000
Offset: 0

Views

Author

Paul Barry, Apr 02 2003

Keywords

Comments

A row of the number array A082038.

Crossrefs

Cf. A082035.

Formula

a(n) = 9*A002775(n) + 3*A001563(n) + n!.

Extensions

Definition and formula corrected by Neven Juric, Jul 01 2008
Showing 1-3 of 3 results.

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

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