A362783 Square array A(n,k) = (n^(2*k + 1) + 1)/(n + 1), n >= 0, k >= 0, read by antidiagonals.

1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 11, 7, 1, 1, 1, 43, 61, 13, 1, 1, 1, 171, 547, 205, 21, 1, 1, 1, 683, 4921, 3277, 521, 31, 1, 1, 1, 2731, 44287, 52429, 13021, 1111, 43, 1, 1, 1, 10923, 398581, 838861, 325521, 39991, 2101, 57, 1, 1, 1, 43691, 3587227, 13421773, 8138021, 1439671

Offset

0,9

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)

Formula

A(n,k) = Sum_{j=0..2*k} (-n)^j.

Example

Array begins:
=====================================================================
n/k |  0    1      2       3         4          5            6   ...
----+----------------------------------------------------------------
0   |  1    1      1       1         1          1            1   ...
1   |  1    1      1       1         1          1            1   ...
2   |  1    3     11      43       171        683         2731   ...
3   |  1    7     61     547      4921      44287       398581   ...
4   |  1   13    205    3277     52429     838861     13421773   ...
5   |  1   21    521   13021    325521    8138021    203450521   ...
6   |  1   31   1111   39991   1439671   51828151   1865813431   ...
   ...

Prog

(PARI) A(n, k) = (n^(2*k + 1) + 1)/(n + 1) \\ Andrew Howroyd, May 03 2023
(Magma) /* as array */ [[&+[(-n)^j: j in [0..2*k]]: k in [0..6]]: n in [0..6]]; // Juri-Stepan Gerasimov, May 06 2023

Crossrefs

Columns k=0..3 are A000012, A002061, A060884, A060888.

Rows n=2..4 are A007583, A066443, A299960.

Main diagonal is A179897.

Sequence in context: A256692 A228637 A352431 * A152795 A338817 A121585

Adjacent sequences: A362780 A362781 A362782 * A362784 A362785 A362786

Keyword

nonn,tabl

Author

Juri-Stepan Gerasimov, May 03 2023

Extensions

a(49) corrected by Andrew Howroyd, Jan 20 2024

Status

approved