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.
%I A362783 #23 Jan 20 2024 15:50:04
%S A362783 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,
%T A362783 1,683,4921,3277,521,31,1,1,1,2731,44287,52429,13021,1111,43,1,1,1,
%U A362783 10923,398581,838861,325521,39991,2101,57,1,1,1,43691,3587227,13421773,8138021,1439671
%N A362783 Square array A(n,k) = (n^(2*k + 1) + 1)/(n + 1), n >= 0, k >= 0, read by antidiagonals.
%H A362783 Andrew Howroyd, <a href="/A362783/b362783.txt">Table of n, a(n) for n = 0..1325</a> (rows 0..50)
%F A362783 A(n,k) = Sum_{j=0..2*k} (-n)^j.
%e A362783 Array begins:
%e A362783 =====================================================================
%e A362783 n/k | 0 1 2 3 4 5 6 ...
%e A362783 ----+----------------------------------------------------------------
%e A362783 0 | 1 1 1 1 1 1 1 ...
%e A362783 1 | 1 1 1 1 1 1 1 ...
%e A362783 2 | 1 3 11 43 171 683 2731 ...
%e A362783 3 | 1 7 61 547 4921 44287 398581 ...
%e A362783 4 | 1 13 205 3277 52429 838861 13421773 ...
%e A362783 5 | 1 21 521 13021 325521 8138021 203450521 ...
%e A362783 6 | 1 31 1111 39991 1439671 51828151 1865813431 ...
%e A362783 ...
%o A362783 (PARI) A(n,k) = (n^(2*k + 1) + 1)/(n + 1) \\ _Andrew Howroyd_, May 03 2023
%o A362783 (Magma) /* as array */ [[&+[(-n)^j: j in [0..2*k]]: k in [0..6]]: n in [0..6]]; // _Juri-Stepan Gerasimov_, May 06 2023
%Y A362783 Columns k=0..3 are A000012, A002061, A060884, A060888.
%Y A362783 Rows n=2..4 are A007583, A066443, A299960.
%Y A362783 Main diagonal is A179897.
%K A362783 nonn,tabl
%O A362783 0,9
%A A362783 _Juri-Stepan Gerasimov_, May 03 2023
%E A362783 a(49) corrected by _Andrew Howroyd_, Jan 20 2024